Yep...you'll get a SC credit for the taxes you had to pay to NC.
1) You need to fill out your entire Federal tax return first ...with everything...every scrap of income and every potential Deduction&Credit.....fully complete and ready to file (but not filed yet). The state parts are meaningless until ALL of the Federal is filled in first
2) then it is critical that you do the NC nonresident tax return next. NC should only be taxing your NC income, but will use your total income to determine the gross tax before ratioing it down based on what % you earned within NC.
3) lastly, you do the SC tax return. SC calculates a tax on all your income from everywhere...but then allows you a credit for the taxes that NC "kept". i.e., if NC refund some of the withholding, then that isn't part of their credit. (which is why you must prepare NC first). OR if you have to pay NC more, then you may get a greater credit. There is some math hand-waving since SC and NC tax rates don't match.......but that's the gist of it.
Print this out and keep in your tax folder for reference next February...don't bother starting until Feb or March of 2020.