By Holly Yan, Susannah Cullinane and Cassie Spodak, CNN

(CNN) -- Even as Florence leaves the Carolinas, the floodwater and death toll keep rising.

The storm once known as Hurricane Florence has already killed 20 people, trapped hundreds more and made parts of the Carolinas impassable. But forecasters say the worst flooding is yet to come.

"This is a monumental disaster for our state," North Carolina Gov. Roy Cooper said Monday. "This is an epic storm that is still continuing because the rivers are still rising."

Residential streets have turned into rivers. Parts of freeways -- dotted with rescue boats -- have morphed into free-flowing waterways.

And the remnants of Florence, now a tropical depression, will likely dump another 2 to 5 inches of rain Monday on central and southeastern North Carolina, CNN meteorologist Michael Guy said.

But even when the rain lets up, don't be fooled. The big concern now is river water gushing downstream, further deluging already flooded cities.

"Catastrophic and historic river flooding will continue for days across portions of the Carolinas," the National Weather Service said.

Now there are fears the death toll will keep climbing. Authorities reported two more deaths on Monday, both in North Carolina.

The body of an elderly man was found by his submerged car Monday morning, the Union County Sheriff's Office said.

And 1-year-old Kaiden Lee-Welch, who was swept away by rushing waters Sunday, was found dead Monday, also in Union County.

Houses turn into islands in the Carolinas

The flooding is so bad in North Carolina that the state's transportation department warned people not to travel in or through the state. Some interstates, including sections of I-95 and I-40, are closed.

Emergency workers have made at least 1,000 swift-water rescues in North Carolina by early Monday, the North Carolina Department of Public Safety said. But many more people need help.

Those trapped in floodwater could also be without power for days.

About 488,551 customers in North Carolina and 16,385 in South Carolina don't have electricity. But the number of actual people without power is far greater, since a single customer can represent an entire family.

Wilmington is still cut off to residents

The coastal North Carolina city of Wilmington, population 117,000, is so deeply submerged that no one could get in Sunday.

By Monday, authorities were able to open one road into the city. But it's not for residents to use to return.

"We do not want evacuees to go back. There's too much going on," Cooper said.

The state's Department of Transportation said it's not clear how long that road will stay open, so authorities are trying to bring in as many supplies as possible.

"We are pushing supplies as hard as we possibly can with the plan that (the road) may not sustain us over the next week," DOT Secretary James Trogdon said.

And supplies such as fuel are in critical need.

The Wilmington-based Cape Fear Public Utility Authority urged residents to fill bathtubs and containers with water in case it doesn't have enough fuel to keep its water treatment plants running.

Pender County, just north of Wilmington, is also running out of fuel, Commissioner Jackie Newton said.

River threatens to swallow Lumberton ... again

In Lumberton, North Carolina -- a city submerged by Hurricane Matthew in 2016 -- residents are bracing for potential disaster as the Lumber River seeps through a patched-up gap in the levee system.

The river is expected to crest around 25.7 feet. If the river gets higher than 26 feet, "all bets are off," city public works deputy director Corey Walters said.

Yet one family riding out the storm on the outskirts of Lumberton said they're not budging.

"I just feel comfortable staying. We have our dogs and our property, so we stay," 57-year-old Kenan Chance said.

Her family's homes are still damaged from Matthew, but they survived. Relatives say whether they stay or go, they'll have damage to contend with.

Chance's father, 84-year-old Rembert Walters, says that if his relatives dispersed to different havens, he'd spend all his time worrying about them.

"We're not going to move until this thing's over. It's going to wipe us out or kill us. Or bury us, or something," he said as floodwater crept upon his porch. "'Cause we don't run every time this thing happened."

'Bring your pets with you!'

Some residents said they decided to stay because many emergency shelters don't accept pets. But those who left without their pets faced the wrath of passers-by and social media users.

Freelance journalist Marcus DiPaola tweeted that he helped rescue six dogs in Leland, North Carolina, after they were left locked in an outdoor cage.

"We got them out, but by the time we left, the water was so high that they would have drowned. BRING YOUR PETS WITH YOU! #HurricaneFlorence," he wrote.

Causes of death include electrocution and fallen trees

Of the 20 deaths linked to Florence, 15 happened in North Carolina and five were in South Carolina. They include:

-- A 3-month-old baby died after a tree fell on a mobile home in Dallas, North Carolina.

-- A man died when a his truck hit an overpass support beam on Interstate 20 in Kershaw County, South Carolina.

-- A man drowned in an overturned vehicle on a flooded road in Georgetown County, South Carolina.

-- Three people died in flash flooding or swift water on roads in Duplin County, North Carolina

-- Two people died in a storm-related fire in Cumberland County, North Carolina

-- A mother and a child were killed when a tree fell on their house in Wilmington, North Carolina

-- Two people died from carbon monoxide poisoning in Horry County, South Carolina.

-- A woman in South Carolina died after striking a downed tree while she was driving.

-- A woman suffered cardiac arrest in Hampstead, in North Carolina's Pender County. When emergency responders tried to reach her their path was blocked by fallen trees.

-- Another person died in Pender County, according to the county's emergency management director. No details were immediately available.

-- A man was killed while checking on his dogs in Lenoir County, North Carolina.

-- Another man in Lenoir County was electrocuted while trying to connect two extension cords.

-- An 81-year-old man fell and struck his head while packing to evacuate in Wayne County, North Carolina.

Where Florence's remnants will go next

What's left of Florence is dragging itself north, dumping heavy rain Monday as it moves into the southern Appalachian Mountains.

On Monday morning, Tropical Depression Florence was centered about 125 miles west southwest of Roanoke, Virginia, the National Weather Service said. It was moving north at 13 mph, whipping 30 mph winds.

Mountainous parts of southern Virginia are now at risk for flooding, mudslides and landslides due to Florence's heavy rains on Monday, said Guy, the meteorologist.

The storm is expected to move north through the Charlottesville, Virginia, area before heading toward the Ohio Valley, hitting West Virginia and western Pennsylvania.

By Tuesday, Guy said, "the remnants of Florence will be pushed towards the Northeast where areas from Northern Pennsylvania through central New York towards Boston could pick up some heavy rain."