Imtissal Samouni, Nawal's mother, told Al Jazeera: "The strikes and the shelling were all around us. It was night time and there was no electricity so we held a candle up to see.
"I tried to take out the placenta but there were more strikes so it wouldn't come out ... and Nawal started bleeding heavily. I cut the umbilical cord with a knife as it was around the baby's neck."
The Israeli army prevented paramedics from entering the area where the family was sheltering for several days, according to the Samouni family.
When they finally escaped, Israeli troops shot at them, Nawal's other children told Al Jazeera, saying the soldiers had looked on them and laughed as they opened fire.
Accounts of what happened to the Samounis and others like them in Gaza during Israel's 22-day offensive on the Palestinian territory are only just beginning to emerge.
Al Jazeera's Sherine Tadros, who covered the war in Gaza as well as the Samouni family's story, said that many Palestinians had approached her with accounts of family members being killed in front of their eyes.
Over 1,300 Palestinians died in the Israeli offensive and homes and infrastructure in Gaza were destroyed.
Israel has also come under criticism for using phosphorus weapons in built up civilian areas.
The UN's nuclear watchdog, The International Atomic Energy Agency, has said it will open an investigation into Israel's alleged use of depleted uranium during its campaign.
On Sunday, Hamas and Israel separately declared ceasefires which continue to hold.
The UN Security Council has issued a statement calling for the ceasefires to be turned into a "durable" truce agreement, calling for guarantees to prevent arms being smuggled via tunnels in Gaza and for Israel to open all border crossings.
The council has also expressed "grave concern" at the humanitarian situation in Gaza.
The US supported the press statement, which came out on Wednesday, having abstained from backing an earlier, legally-binding resolution adopted by the security council on January 8.