Florence diminished from hurricane strength as it came ashore on Friday, but the large storm's slow progress across the two states could leave much of the region under water in the coming days, according to forecasters.
Police confirmed the fatalities on Twitter, saying the father of the child was being transported to a local medical centre to be treated for his injuries.
Director Tom Collins says the woman in Hampstead had a heart attack Friday morning, but emergency crews could not get to her because of downed trees in the road.
Florence was inching along Friday night, trapping people in flooded homes and promising days of destruction and human suffering.
"[It's] very eerie, the wind howling, the rain blowing sideways, debris flying", Orsa, who lives nearby and fears splintering trees will pummel her house, told The Associated Press.
That kind of scenario is likely to repeat itself all over communities in Eastern North Carolina, as swollen rivers flood towns and the pouring rain adds to the misery.
As Tropical Storm Florence continues its slow assault on the North Carolina coast, some county sheriffs are grappling with another problem amid the mass flooding: looters.
A day after Florence blew ashore in North Carolina with 90 miles per hour (145 kph) winds, Coast Guardsmen, Marines and other rescue crews used helicopters, boats and heavy-duty vehicles to reach scores of people trapped on rooftops or otherwise caught in the floodwaters.
The National Hurricane Center said as much as 40in (102cm) was expected on the southeastern coast of North Carolina and part of northeastern SC.
Thousands of South Carolinians continue to remain without power.
Some towns have already been soaked by more than 2 feet (60 centimeters) of drenching rains, and forecasters warned that totals could reach 3 1/2 feet (1 meter), unleashing floods well inland through early next week.
Firefighters in North Carolina took a moment to kneel and pray at the site where a mother and baby were killed by a tree that fell down during Hurricane Florence. "You're going to have flooding miles and miles inland", the center's director, Ken Graham, said. In perspective, Florence could drop up to eight months of rain in two or three days.
One of the rescuers in New Bern was Jason Weinmann, a retired Marine who has a military troop transport vehicle he bought at a government auction.
Some parts of North Carolina have already seen surges as high as 10ft (3m) in places.
"Right now we've rescued over 400 people".
The body of a 77-year-old man, also in Kinston, was found by his family at his home, and it is believed he died when he was blown down after going outside to check on his hunting dogs, Dail said. One team from Maryland helped with about 40 rescues in New Bern starting Thursday, member Mitchell Rusland said. "So, even if it was just a tropical storm and trees went down we'd have a hard time getting here".