I was wondering if I had to pay the NC state tax if it was for working as a student doing work study as part of my financial aid

You would need to prepare a North Carolina tax return if your federal income is $8,750 or more for a single filer. You would file as a non-resident if you are away at college temporarily. 

What do I do if I got a full time job in late 2020 in a different state where I earned more than $8,500? Would i still need to declare the less than $2,000 i earn in NC?

If your parents claim you and you are a student, then your state of residence is where your parents live. You must file a tax return for your state of residence that includes all income, based on its filing requirements. Each state has different minimums.

In what state did you earn additional money? What state is your resident state?