The story was the same in the southern city of Khan Younis.
"Our clothes, mattresses and blankets were flooded," said Nihad Shabat, as she tried to dry out her possessions there on Monday.
Her family has been sleeping inside a shelter made of sheets and blankets.
"We're worried about getting flooded again. We cannot afford to buy a tent."
A recent UN report found that across Gaza more than 80% of buildings had been destroyed and 92% in Gaza City.
According to the NRC - which has long led the so-called Shelter Cluster in Gaza, made up of some 20 non-governmental organisations (NGOs) - about 260,000 Palestinian families, or about 1.5 million people, are in need of emergency shelter assistance, lacking the basics to get through winter.
The NGOs say they have been able to get only about 19,000 tents into Gaza since the US-brokered Israel-Hamas ceasefire took effect on 10 October.
They say they have 4,000 pallets of aid - containing non-food items, including tents and bedding - blocked from entering. Supplies that have been bought are currently stuck in Egypt, Jordan and Israel.
Jan Egeland blames what he calls "a bureaucratic, military, politicised quagmire" running "counter to all humanitarian principles" for the hold-up.
In March, Israel introduced a new registration process for aid groups working in Gaza, citing security reasons. It requires that they give lists of their local Palestinian staff.
However, aid groups say that data protection laws in donor countries prevent them from handing over such information.