Anne-Marie Cockburn wrote the following words on 21 July 2013: "My 15-year-old daughter died yesterday. I watched them try to save her. They pumped her chest and drilled something into her leg, but I knew she was already dead on arrival at the hospital. They elevated her arms, but I don't know why: her eyes were half-open and she was way beyond the clouds and stars already."

The previous morning, a sunny Saturday, Anne-Marie was the happy mother of a healthy child. She and Martha were close, perhaps in a way only a single mother and her only daughter can be. It was just the two of them in their cosy flat in Oxford and they did everything together. Earlier that week they had been to Ikea to buy new stuff for Martha's bedroom; the following weekend, they were off to Bristol. That day, Martha went kayaking with friends on a lake across town and Anne-Marie went shopping.

But by Sunday morning, Martha was dead: Anne-Marie woke up to an entirely changed identity. "There's no word for what I'd become – maybe it's too terrible a situation to have a word for," she says. "I'm not a widow or an orphan or a divorcee – they all have a word.

"To describe what I am, I need nine words: 'I'm a single mother whose only child is dead.'" Today, nearly six months on, she thinks of herself as a "non-practising" mother; because she'll always be a mother, the woman who bore Martha. She's made up a word to describe herself, too: smothered. "That's 's' for 'single', and then 'mother', and 'ed' is for 'expired daughter'," she explains.

Smothered could also describe the effect of losing her child. It could explain the impact of the magnitude of grief on this slight, 42-year-old woman who says she never really looked for another partner after finding herself alone with a 10-month-old baby because Martha was enough.

Yet the last thing grief has done to Anne-Marie is smother her. In many ways, she says, she feels more alive than ever. It's as though her antennae are twice as sensitive and she's seeing the world in extra-sharp focus because of what she's been through.

She notices every detail, is attuned to every nuance that underlines the gulf between the way she was, and the way she is now. "The other day I looked down at a bag with someone's shopping, and I saw a box that said family tissues," she says. "I thought, I don't need those any more, I can just buy packets for one."

Another time she and a friend went on a train journey that they'd usually have made with Martha. "I was about to get out my family railcard and then I stopped and said, I can't use this any more, can I? And they said, you need a child to travel with you to use that. And I thought, I don't have a child to travel with any more."

This is red-raw, unadulterated, up-close grief: and what's remarkable about Anne-Marie is that she's chosen to share the immediate grief of the early hours, days, weeks and months – and of now – with the rest of us.

Anne-Marie Cockburn: 'If I just close my eyes I can feel the brush of her lips against my cheek.' Photograph: Graeme Robertson for the Guardian

Writing has been her therapy since the day Martha died. "Writing it down felt right," she says. "I've always written a diary and when I started writing this down, it poured out. On the second day my parents physically took the notebook and pen out of my hands and said, you've got to have a shower. I was just writing, writing."

Now, when she reads what she wrote in those first few days, it's as if she's finding out what she was doing for the first time. "You forget everything in the shock of early grief. Writing it down straight away is the only way of remembering what happened and I need to remember it because I need to make sense of it," she says.

She is publishing her diary because of the way Martha died. What happened on that July day by the lake in Oxford was that Martha took what she thought was MDMA, better known as ecstasy. Shortly before 12.45pm, Anne-Marie texted her daughter to tell her the name of the hotel she'd booked in Bristol for the following weekend. Martha responded simply: "Cute."

"That meant she approved," smiles Anne-Marie. "She was looking forward to going away."

Half an hour later, a number she didn't recognise flashed up on Anne-Marie's phone. She answered and the world as she'd known it for 15 years ended. "It was a woman calling. She said: 'Your daughter is gravely ill and we are trying to save her,'" Anne-Marie remembers. A friend drove her to hospital, but Martha hadn't arrived. "They told me they had no notification of the incident, and it was only when I said that the woman in the park had told me they'd called the air ambulance that they realised how serious it was and showed me to a side-room."

When the ambulance arrived (Martha was brought by road in the end, because she wasn't stable enough to travel by air), Anne-Marie was ushered into the emergency room where the crash team was desperately working on her. "But I knew, the second I saw her, that she was dead," says Anne-Marie. In her book, she describes what happened next. "I was calling to her in the tone I last heard when I gave birth to her." And then: "I couldn't breathe once they announced what I already knew: my fingers and toes were tingling. They put me on a wheeled chair and asked me what I wanted to do. What do I want to do? I don't know what to do – what do you do in a situation like this?"

In many ways that question has become a daily mantra in Anne-Marie's mind. Just as there is no name for her condition, so there is no blueprint, no strategy, no recipe for dealing with a loss like hers. There are no children to carry on for and there's no partner to keep her going.

All that makes sense to Anne-Marie is to document the experience in the hope that others will learn from it. She believes this is happening already among Martha's friends in Oxford. "Some say they'll never touch drugs now – they didn't realise how dangerous something like Ecstasy could be."

Martha and Anne-Marie.

She hopes parents of teenagers will ask more questions, take the threat of drugs more seriously. "Because it wasn't just Martha – so many teenagers are buying and taking drugs. I honestly believe that if it could happen to us, it could happen to anyone. She couldn't have imagined that this could mean the end of her life, at the age of 15."

Almost half a year on, Anne-Marie is about to go through her first Christmas and New Year in her new, "smothered" state. On what would have been Martha's 16th birthday, on 30 October, a group of her friends joined her in the park where she died, and at 6.41am, the exact time she was born, they lit lanterns by the lake in her memory. Anne-Marie feels a responsibility to be there for Martha's many teenage friends, for whom her death could hardly have been more shocking. "So many of them have been deeply affected by it – I want to help them find peace and to remember her."

Remembering Martha is never difficult for her mother. "If I just close my eyes I can feel the brush of her lips against my cheek," she says. The girl she recalls was quirky and fun and cheeky and happy – and, in the last few months of her life, amid the tumult of adolescence, a bit rebellious and restless. She loved music, and was hoping to go to her first festival next summer. Two days before her death she went on a school trip to the Natural History Museum; she was keen on science, and might have gone on to do engineering. In the short term, though, her big ambition was to get her mum to say yes to a day shopping in London with her friends.

Anne-Marie has memories, too, of travelling the world with Martha. "I'm so grateful that we saw so many places, went on so many trips," she says. "When I was 15 I'd only been to Germany: but Martha had been to America and Croatia, France and Greece, Ireland and Italy, Spain and Singapore. She rode on a camel in Egypt, went on an elephant in Bali, snorkelled on the Great Barrier Reef. She lived for 5,472 days, seven hours and 36 minutes, and her life was full of adventure – and I'm so happy I shared so many of those adventures with her."

How will Anne-Marie live her life, now that her daughter is gone? "I could have become a crazy cat lady," she says. "I could have had a breakdown. I could have just given up and never gone out again.

"But Martha thought life was amazing. And I still think life is amazing. I wish it could be amazing with her still in it, but it can't. It can only be amazing without her. And I'm going to do my best to make it that."

Book extract: The first 36 hours after my world ended

My eyelids finally stopped fighting the sleep last night and I slept deeply and soundly. I woke up early. My heart is beating, but it pangs with the loss, knowing that I will always miss her. I missed her even when she was only away for a few hours, so this type of "missing" is peculiar, unnatural.

Getting used to her not being here goes against what every cell in my body feels. I am a mother, that is what I do. Mothers care and plan ahead, mothers nurture and nag you to tidy your bedroom. Mothers tell you to shower after you've been swimming in the lake. Martha would make excuses and go to bed with the grit of the day on her.

I'll never get to nag her again, I'll never get to tell her that her room is a mess … oh how I wish I could nag her again and to hear her excuses … "I'll do it later, I'll shower after kayaking tomorrow." I'd be both bemused and irritated by this, but that is a luxury now that I'll never get to practice again. I am still a mother, but not a practising one. I have all these mothering skills that I know will always be useful in my life, but their immediate purpose is no longer what they'll be used for.

So I did what I needed to do today, I went online and started looking at coffins: what would she like, what would Martha choose? She was far from traditional, she wouldn't want anything gimmicky either. The answers come to me gently. I know that whatever is chosen, it'll be lovely but really – does it matter that much? The true meaning of life has hit me like a bolt of lightning and the previous version of me now seems trivial – but it's a shame that this had to happen in order for this stoic version of myself to surface.

I'm going through her clothes today, to choose an outfit to dress her in. She liked to wear crop tops and denim shorts that were more revealing than any parent is comfortable with – "pull those shorts down" I hear the previous version of myself say.

Today I say, "Martha, what would you like me to dress you in – what outfit is the right one to represent you for the very last time?" It definitely won't be denim shorts and a crop top, but it'll be something that'll show my precious daughter off beautifully.

Martha, if you are with me now, please hold my hand and guide me to show me what you want. I love you so much and don't know where to channel this love now. I have too much of it and it was all for you. I'll give some to myself now as I need it, I'll give some to family, friends and strangers, but I've still got too much left. It feels like a burden, but I know it'll get easier.