Assuming you're taking mostly I-95 up, I would personally suggest you take a slight detour at some point and stay somewhere on the coast, either Myrtle Beach
In Wilmington, you can check this list of hotels:https://www.trippy.com/popular/Hotels/Wilmington-NC
You need to call the specific location to find out if it's pet-friendly and if there are charges for pets, but generally Red Roof, Comfort Inn, Holiday Inn, and Best Western have pet-friendly hotels.
For Myrtle Beach, check this list:https://www.trippy.com/popular/Hotels/Myrtle-Beach
Here, I'd call the Fairfield Inn, La Quinta, or Quality Inn for possible pet-friendly hotel chains.