For little Sayef, there will be no Arab Spring. He lies, just 14 months old, on a small red blanket cushioned by a cheap mattress on the floor, occasionally crying, his head twice the size it should be, blind and paralysed. Sayeffedin Abdulaziz Mohamed – his full name – has a kind face in his outsized head and they say he smiles when other children visit and when Iraqi families and neighbours come into the room.

But he will never know the history of the world around him, never enjoy the freedoms of a new Middle East. He can move only his hands and take only bottled milk because he cannot swallow. He is already almost too heavy for his father to carry. He lives in a prison whose doors will remain forever closed.

It's as difficult to write this kind of report as it is to understand the courage of his family. Many of the Fallujah families whose children have been born with what doctors call "congenital birth anomalies" prefer to keep their doors closed to strangers, regarding their children as a mark of personal shame rather than possible proof that something terrible took place here after the two great American battles against insurgents in the city in 2004, and another conflict in 2007.

After at first denying the use of phosphorous shells during the second battle of Fallujah, US forces later admitted that they had fired the munitions against buildings in the city. Independent reports have spoken of a birth-defect rate in Fallujah far higher than other areas of Iraq, let alone other Arab countries. No one, of course, can produce cast-iron evidence that American munitions have caused the tragedy of Fallujah's children.

Sayef lives – the word is used advisedly, perhaps – in the al-Shahada district of Fallujah, in one of the more dangerous streets in the city. The cops – like the citizens of Fallujah, they are all Sunni Muslims – stand with their automatic weapons at the door of Sayef's home when we visit, but two of these armed, blue-unformed men come inside with us and are visibly moved by the helpless baby on the floor, shaking their heads in disbelief and with a hopelessness which his father, Mohamed, refuses to betray.

"I think all this is because of the use by the Americans of phosphorous in the two big battles," he says. "I have heard of so many cases of congenital birth defects in children. There has to be a reason. When my child first went to the hospital, I saw families there with exactly the same problems."

Studies since the 2004 Fallujah battles have recorded profound increases in infant mortality and cancer in Fallujah; the latest report, whose authors include a doctor at Fallujah General Hospital, says that congenital malformations account for 15 per cent of all births in Fallujah.

"My son cannot support himself," Mohamed says, fondling his son's enlarged head. "He can move only his hands. We have to bottle-feed him. He can't swallow. Sometimes he can't take even the milk, so we have to take him to hospital to be given fluids. He was blind when he was born. In addition, my poor little man's kidney has shut down. He got paralysed. His legs don't move. His blindness is due to hydrocephalus."

Mohamed holds Sayef's useless legs and moves them gently up and down. "After he was born, I got Sayef to Baghdad and I had the most important neurosurgeons check him. They said they could do nothing. He had a hole in his back that was closed and then a hole in his head. The first operation did not succeed. He had meningitis."

Both Mohamed and his wife are in their mid-thirties. Unlike many tribal families in the area, neither are related and their two daughters, born before the battles of Fallujah, are in perfect health. Sayef was born on 27 January, 2011. "My two daughters like their brother very much," Mohamed adds, "and even the doctors like him. They all take part in the care of the child. Dr Abdul-Wahab Saleh has done some amazing work on him – Sayef would not be alive without him."

Mohamed works for an irrigation mechanics company but admits that, with a salary of only $100 a month, he receives financial help from relatives. He was outside Fallujah during the conflict but returned two months after the second battle only to find his house mined; he received funding to rebuild his home in 2006. He watches Sayef for a long time during our conversation and then lifts him in his arms.

"Every time I watch my son, I'm dying inside," he says, tears running down his face. "I think about his destiny. He is getting heavier all the time. It's more difficult to carry him." So I ask whom he blames for Sayef's little calvary. I expect a tirade of abuse against the Americans, the Iraqi government, the Health Ministry. The people of Fallujah have long been portrayed as "pro-terrorist" and "anti-Western" in the world's press, ever since the murder and cremation of the four American mercenaries in the city in 2004 – the event which started the battles for Fallujah in which up to 2,000 Iraqis, civilians and insurgents, died, along with almost 100 US troops.

But Mohamed is silent for a few moments. He is not the only father to show his deformed child to us. "I am only asking for help from God," he says. "I don't expect help from any other human being." Which proves, I guess, that Fallujah – far from being a city of terror – includes some very brave men.

Fallujah: A history

The first battle of Fallujah, in April 2004, was a month-long siege, during which US forces failed to take the city, said to be an insurgent stronghold. The second battle, in November, flattened the city. Controversy raged over claims US troops had deployed white phosphorus shells. A 2010 study said increases in infant mortality, cancer and leukaemia in Fallujah exceeded those reported by survivors of the atomic bombs dropped on Hiroshima and Nagasaki.

Tomorrow: The doctors fighting to improve the lives of Fallujah's suffering children