If you go through Columbia, SC and pick up I-77 to Charlotte to I-85 to I-40 that should be fine now, I think. The flooding in NC is mainly on I-95 and east, including I-40 east of I-95. I _think_ I-77 through SC should be okay, but check with the SC forum or the SC DOT website.
Joy's link is the best for NC road conditions.
We had some flash flooding in the Cary area last night, but that should all be cleared up by now.Edited: 18 September 2018, 03:18
You cannot go on I-95, though. It's completely flooded over (not even down to 1 lane) as is I-40 east of I-95. Rivers are expected to crest on Tues so it will be a little while before I-95 and I-40 going to Wilmington are back operational.