When Hayley Williams was nine, her dad often took her go-karting at Ultimate Fun World in Mississippi. The harder she pressed the accelerator, the more it alleviated her growing pains. She would spend all day driving until she forgot about the ache. “I thought I was gonna get taller,” she says.

Williams is now 31, and all of 5ft 1in tall. Sitting in a London hotel room, pastel tie-dye leggings breaking up her black attire, she lets out a delighted and mortified howl as I read the karting entry from her old LiveJournal and relate it to how she continued to ride out her pain: first as the songwriter and vocalist of the Nashville pop-punk band Paramore, she was plagued by a carousel of members quitting in high dudgeon, inevitably smearing the singer on their way out; and, later, as a wife in a marriage she knew she shouldn’t have gone through with. On Paramore’s first tour as a united front, for their superb 2017 album After Laughter, she preached self-acceptance while on stage, but drank to mask her depression.

Williams thinks back to the karting. “A metaphor!” she hoots.

Her debut solo album, Petals for Armor, has an insular, Radiohead-like mood, which is the opposite of her output in her incendiary day job. Given that Paramore has only had a stable lineup for three years, it may seem like bad timing for a solo venture, but, at the end of their last tour, Williams, the band’s guitarist, Taylor York, and the drummer, Zac Farro, realised that to endure as a band they needed to nurture their friendship off the road. With no Paramore plans, Williams was confronted by a feeling that had started bubbling up on tour. She recalls her disbelief: “‘I think I’m really angry?’”

Cinnamon.

Given that Williams is a figurehead in a scene called emo – as in emotional – her alienation from her feelings may seem strange. She has never minced her lyrics, and has a pugnacious stage presence. Also, she didn’t lack reasons to be mad: before releasing After Laughter, she had left her husband of two years (and partner of 10), New Found Glory’s guitarist Chad Gilbert.

Yet selling rage is easier than embodying your own, especially as a young woman who didn’t need to give ex-bandmates and authenticity bores extra ammo to undermine her. “It’s not becoming, you know?” Williams says. “One of my biggest healing moments was realising that a lot of my depression was misplaced anger. I really forced it inward, on myself, and it made me feel shame all the time.” Anger, she later discovered, could be an energy; a recognition of self-worth. “It helped me understand things that happened throughout my life that weren’t right.”

It started with her first memory – of the fight that instigated her young parents’ divorce. “They were kids,” she shrugs. “They made a mistake. It’s not really something to be angry at. But when I did some therapy, I realised I was four years old and I thought it was my fault.” She came to realise that everything stemmed from that moment: “I always wanted a family.”

What happens in our brains often manifests physically if we don’t take care of it

Hence Paramore. Hungry to start a band, Williams couldn’t find anyone to play with as a preteen in Mississippi. In 2002, she and her mum fled her “nightmare of a stepfather” to Franklin, Tennessee. They lived with friends, in a hotel, a trailer, an apartment furnished with donations from a church care group. Williams was bullied for her accent, so she started home-schooling with a weekly in-person tutorial. On day one, she met Farro, who introduced her to the boys with whom she would form Paramore. By 2005, they were emo royalty, as much for their soaring choruses as the intra-band drama. Their ever-changing lineup cut Williams deeply: “I was trying so hard to keep a family together.”

It was the same in her relationship with Gilbert, she says, which started in 2008. She wanted to mirror the one steady relationship in her life: her grandparents, who met at age 12 and stayed together. Therapy later made her realise she had also picked a partner with whom she could relive the trauma of her parents’ marriage. “I was in a very unhealthy relationship, and I just kept thinking: ‘I can fix it this time.’”

She is discreet about their relationship to avoid public recriminations. “He probably looks at me like the villain,” she says enthusiastically. “Throwing around my version of someone else’s story doesn’t feel fair, which is funny because I don’t necessarily think it should be fair. Especially not after the shit I went through.” Williams knew she couldn’t save the relationship – or that it couldn’t save her – before their wedding in 2016. She didn’t want to get married. But she liked the tidy conclusion. “I wanted the whole thing – the family – and I thought I might even stop doing music for a while to do that.” It would never have been a consideration had she felt supported. “Give up the thing that’s the most precious to me? Are you kidding me?”

On Paramore … ‘I was trying so hard to keep a family together.’ Photograph: Lindsey Byrnes

After the couple split, her best friend reminded her of the morning of the wedding. As he helped Williams with her Vera Wang dress and Dr Martens boots, she wouldn’t stop picking herself apart. It was out of character, he said, for someone who usually has a pretty carefree attitude to her appearance. “When he said that, I missed myself,” says Williams. “Because when you have so much shame, you don’t want one person to see a fleck of a problem because that could be the floodgate opening.”

Williams’ subconscious had started barging its way out as she wrote After Laughter – particularly on Caught in the Middle, a satire of her knack for self-sabotage. “It is terrifying to live in that reality because you realise you are the villain,” she says. “You just keep fucking up your own story on purpose because you’re scared for something to go right and still mess up.” She developed rashes, stopped eating and her adrenal activity flatlined. She left the relationship, abandoned her possessions and moved into a Nashville cottage with a mattress on the floor, patio furniture lent by her new neighbours and a bat infestation problem that cost $10,000 to fix.

The After Laughter promo cycle was just beginning. When Paramore shot the first two videos, Williams weighed six and a half stone. “It wasn’t until I saw the pictures that I was like, there’s no hiding that I’m not OK now,” she says. “And part of me enjoyed that – if people know I’m not OK, they won’t get too close.”

Her bandmates coaxed her to eat after the tour started. Then her coping mechanisms went into overdrive. Williams’ ex is straight-edge, so she hadn’t drunk alcohol for most of her 20s. “But it wasn’t really about me,” she says. “It was about people-pleasing.” Her divorce and slow acceptance of her emotions left her downing tequila before the encore, “looking to break free from a prison that I’d put myself in and to also forget at the same time”.

She wouldn’t describe herself as depressed, even though she had felt suicidal. “What I hated was at the time it was still sort of new to see the word ‘depression’ – it became such a hot-button word, almost clickbait?” she says tentatively. “And it scared me to become part of that conversation, especially if I wasn’t even sure what was actually going on with me.”

It clicked once she got home. She started therapy and replaced the patio chairs with real furniture. The new album features an intimate, offbeat song called Cinnamon, about her home and the pleasure of eating breakfast in the nude. “I lived in a trailer for months when my mom and I were running away,” she exclaims. “To be able to have your own space is such a mark of: this is who I am, and this is my reprieve.”

Having felt physically and emotionally “incongruent” for so long, Williams is evangelistic about recognising “that what happens in our brains often manifests physically if we don’t take care of it”. She mentions a spate of pop stars (including Justin Bieber and Selena Gomez) with autoimmune diseases. “I’m a firm believer that the reason we’re seeing this is like, how long have you repressed some shit? ’Cos it’s real.”

In the studio in 2017. Photograph: Bill McCay/Getty Images

Vulnerability has become her greatest “weapon of protection”, taking the pressure off: “You don’t gotta expect me to be great!” The introspective Petals for Armor is more exposing than any Paramore record, addressing her relationship and the “disgusting” abuse endured by older female relatives. It establishes her place in a feminine lineage that she hadn’t previously felt comfortable claiming. Whenever Williams struggles with shame around her divorce, she remembers with no small amount of awe that she wouldn’t have this career were it not for the strife that started in her childhood.

Rather than regret her past, she hopes to highlight the power of female anger. “Women’s rage has changed many things in this world,” she says. “We’ve been able to effect progress in so many arenas.” The world in 2020 doesn’t exactly want for hot tempers. But, Williams says, anger is usually trying to teach you something. “It doesn’t have to all be ignorance and hate speech and bullshit.”

• Part one of Petals for Armor is out now on Atlantic. The full album is released on 8 May