I am not licensed to practice in NC so this answer is general in nature. For a specific answer consult a NC attorney.
In criminal cases, my state of CA has free appellate lawyers if you want to use one. I'd almost bet that your state has a similar program. This does not re-open your case but gives you a shot on appeal. Other strategies: move to withdraw the plea (lawyer needed) or after the appeal file a writ of habeas corpus. Many people do the latter on their own without a lawyer but you must exhaust your appeals first.
You could move to withdraw your plea. But even if the judge finds that there are good grounds to grant that motion does not mean your case is over. It just means you are back to square one and you will then have to go to trial. I don't practice in NC but you may be able to talk to an attorney there who can give you an idea how expensive this is, including a trial. Good luck.
Usually when you enter a plea you waive your right to appeal. You can withdraw a plea in Florida within 60 days. Check with a local attorney.
The only way to reopen a criminal case is to file a motion for appropriate relief in Superior Court. Your motion must allege compelling reasons for revisiting a case where you were represented by counsel and accepted a plea bargain.