The International Committee of the Red Cross (ICRC) said the paramedics found "shocking" scenes of wounded people huddled together in houses among dead bodies, weak after having had no food or water for several days.
In one home, the agency said, four small children were found sitting close to their dead mothers, "too weak to stand on their own".
It is not clear if Sameh and Ahmad were in that particular house - it may be that the unconscious Fatima was initially thought to be dead - but she says she and her toddlers were among those who had a long wait for help.
The ICRC has accused the Israeli military of failing to live up to its obligations under international law to facilitate the evacuation or to care for the wounded.
The agency said it had been requesting safe passage for its ambulances to access the neighbourhood since 3 January, but only received permission to do so from the Israeli Defence Forces (IDF) four days later.
The ICRC said the wounded had to be transported about a kilometre on a hand-pulled donkey cart because large earth walls erected by the Israeli army had made it impossible to bring ambulances into the neighbourhood.
Katarina Ritz, the ICRC's head of mission in Jerusalem, said experienced Palestinian emergency workers wept at the scenes they were confronted with.
She said Israeli troops were within about 100m of the houses in question, and that the ICRC believes the soldiers "must have been aware" of the presence of the wounded people, because of repeated requests from aid agencies for access.
The Israeli military said it was investigating the case. It said it is "engaged in a battle with the Hamas terrorist organisation that has deliberately used Palestinian civilians as human shields".
And it stressed it works in "close co-operation with international aid organisations during the fighting, so that civilians can be provided with assistance".