I have looked into the college I want to go to (UNC Chapel Hill, in-state student), and I have noticed that my GPA is above their average, but my SAT scores are below their average. I'm scoring around a 1650 on the 2400 scale. I also tried taking the ACT, but I scored in the same range. I have pretty good extracurriculars and have taken almost all AP and honors classes. Is my low SAT score going to prevent me from getting in?
Your SAT score is low enough to present you with some problems in the Chapel Hill admissions process. Since you're an in-state student, you have a better chance of admission overall (more than half of applicants from in-state were admitted last year, as compared to only 19 percent of out of state applicants), but I would still put more effort into raising your score. It's below the 25th percentile for admitted students, so it's in a somewhat dangerous place. If you have time, I would strongly recommend retaking the SAT.
My main piece of prep advice is to take lots of practice tests and thoroughly review your mistakes. It sounds like you're a high-achieving student who has trouble with the pressure of standardized tests. The more comfortable you are with the format, the more likely it is that you'll improve your score. If you feel you've done all you can on your own, I'd recommend seeking out a tutor or prep course that can give you new strategies for improvement. If you find that you still can't improve your score, you should work on strongly emphasizing other achievements in your application and writing an excellent essay.