You would be forgiven – if you have followed the news lately – for thinking that the Syrian crisis is all about arms and ammunition: who should give what to whom and who shouldn't, who is backing whom and who isn't.

But missing from these discussions are the Syrian children, who are not made of steel, and who are facing desperate and harrowing conditions.

I have just returned from the north of Iraq, a region that has not been making headlines in this emergency. I travelled there with Unicef, the world's leading children's organisation, and met young refugees who had lost everything. Many had seen loved ones killed. Every child had been forced to abandon their home, their friends, their school and everything they knew.

This is a story of human tragedy – not a story of faceless war. Every single Syrian child has been touched by this conflict. When I visited Domiz refugee camp, I heard stories of terrifying journeys out of Syria. These journeys would have been a terrible prospect for any adult, but these tales were coming from the mouths of kids under 10.

Nine-year-old Xalel Abdulhamed from Damascus explained how he had run for his life with his mother, brother and sisters after fighting broke out in their area. They spent days travelling to Iraq, sleeping on the streets, under fear of attack. Xalel had been so scared he was still unable even to go to the toilet alone at night.

Another family, with 10 children, had fled Syria on foot under gunfire – clinging to the few possessions they could carry. A mother of three, Lamaa, was so desperate that she made the journey to Iraq when she was nine months pregnant. Under such stress, a pregnant woman is at risk of going into labour or miscarrying. But Lamaa took the risk, rather than keep her two other children in Syria.

On arrival at camps such as Domiz, the refugees' problems are far from over. The days are unbearably hot. Tents and ad hoc structures advance in rows, coated in dust. The air tastes like baked earth. The homes of many refugees might as well be saunas, as they scorch in the 45C heat.

In conditions like these, what do humans need to survive? Water – and lots of it. But these children don't have enough water that is safe to drink. Xalel and his family use plastic containers to fetch enough to fill their small tank. They won't waste one drop. The camp was designed for 15,000 people but now 45,000 are crammed within its borders. In such packed and sweltering conditions, the risk of becoming dangerously dehydrated is huge, and the threat of an outbreak of disease is only too real.

Shockingly, the children in the camp could be considered the lucky ones. Three-quarters of Syrian refugees are living in urban areas – sometimes in improvised settlements, sometimes in overcrowded rented flats.

About a mile from the border of Domiz camp, I met Dala and her two children living with two other families in a converted animal shelter. Bombing in her region and a breakdown in services including power, police and health, led to lawlessness that put her children in real danger. She picked up her two-year-old son and seven-year-old daughter and did the only thing she could to protect them – she ran.

Nine out of 10 refugee children in this area do not attend school, and Dala's daughter is one of them. She misses her teachers and her friends in Syria. She is unwell from the effects of the dust and the heat.

Unicef is doing everything it can to get vital supplies to children and their families who need aid – including water, vaccinations and education. But the numbers are huge – refugees in Iraq have tripled in the past six months and are expected to double again to 350,000 by the end of the year. Resources are at breaking point. Unicef has only a third of the money it needs to deliver supplies to people who desperately need them.

What concerns me most is the lack of education. This is about children's futures. In Syria these refugees were going to school, just like children in the UK. But their education has been cut off. There aren't enough schools to go around and thousands of children have no classroom to go to. Schooling is everything. Without it, how can you think of getting a job? How can you even fill your day? And, in these most extreme of circumstances, education is critical to help children understand what is happening in their country.

In May, the heads of the five major UN agencies – including Unicef – called on governments to use their influence to insist on a political solution to this horrendous crisis being found before hundreds of thousands more people lose their homes, their lives and their futures.

I hope this political solution comes quicker than some are predicting, for the sake of Syria's children. However, in the meantime, we must do everything we can to support aid agencies to help children deal with the daily reality of the conflict.

Providing humanitarian relief must be our number one responsibility. If you have ever wondered what happens to the money you donate, I can assure you it doesn't go into a hole. It provides potentially life-saving supplies such as clean water – crucial in the heat of Iraq. For £5 (the price of two or three cups of coffee), Unicef can provide safe drinking water for a family of seven for a week.

Aid also provides children with an opportunity to try to recover part of their childhood. I visited a special centre built by Unicef called a Child Friendly Space. It is specifically designed to help children process their experiences, which are often too horrific to imagine. Hundreds of children come here to use the play area and learning centre.

No matter what they have been through, they can go on the swings, play football and get back into being kids. Psychologists and social workers are on hand to offer support to anyone showing signs of distress.

Refugees need support to put back together their lives as best they can. When peace comes, they can go home. In the meantime, we don't want people to fall into a hellish well of despair.

Soon, one million Syrian children will have fled their country and will be struggling to live as refugees. Already, around three million children within Syria are in desperate need of humanitarian assistance. We need to help the aid flow, and we need to stop an entire generation of Syrian children being lost to war. Remember, just £5 could provide water for a week for a family of seven, so please text the word DONATE to 70099 to give £5 now, or visit unicef.org.uk/eddie.