UNC is probably very unlikely (C’s & D’s, class rank and Wake County won’t help you) but maybe your essay and LOR’s would be compelling to whomever reads your application? You never know unless you apply but I would temper your expectations accordingly and if you’re accepted, you’ll be all the more excited. Same with UVA (is cost an issue? UVA will be very expensive for OOS student).
11 AP’s and AP Scholar are good but they may wonder what happened with the C’s & D in the science & math.
NC State would be a reach too, I’m afraid. It’s always been tough for the STEM majors, but now business-related majors are becoming more popular and a tougher admit as well. I don’t know anything about Poly Sci there. Does your high school use Naviance or something similar with scattergrams that you can check to see how students from your high school with similar stats did?
Continue to work on your essay and turn it from “Good” to “Great” (both UNC & NC State have supplemental essays, so make those exceptional), figure out a budget and search on this site for additional safeties and targets in NC & out of state that match your budget. Most colleges have business and poly sci programs, so there should be many to choose from depending on how far you want to travel.
Another possibility is trying to transfer to NC State or UNC after freshman year. I know two students who did that from UNCW. You would have to crush your freshman year GPA though. If you go business, be aware that UNC’s business school is a very competitive admit. You could transfer and not get into the business school there (you could possibly fall back on poly sci).