You are non-residents of NC. For state tax purposes, you remained a resident of VA until you moved into your new domicile in SC. At that point you became residents of SC. Your domicile is your fixed, permanent home. An apartment rented for a temporary purpose does not constitute a domicile.
Here is Virginia's rule on changing domicile:
In order to change from one legal domicile to another legal domicile, there must be (1) actual abandonment of the old domicile, coupled with an intent not to return to it, and (2) an acquisition of a new domicile at another place, which must be formed by personal presence and an intent to remain there permanently or indefinitely. https://www.tax.virginia.gov/laws-rules-decisions/rulings-tax-commissioner/16-125
So for 2019 you must file a part-year resident VA return, a part-year resident SC return, and a non-resident NC return. Note that your income from NC is taxable by both NC and VA. You'll be able to take a credit on your VA return for the taxes paid to NC, so you won't be double-taxed.
In TurboTax, be sure to complete the non-resident return first, before doing the other states.
Are (or were) we NC residents?
It essentially doesn't matter. You will have to file returns in all 3 states and pay tax on the income you received in each state. For sure, you will file a part resident return in both VA & SC. It's not clear, to me, if you should file NC as a part year resident or non resident. I would file as a part year resident, to avoid the possibility of some minor double taxation If you are a non resident, you have to report your NC income to both VA & NC. VA will give you a credit, for what you pay NC, but sometimes it's not 100% credit.