If your stay in New York was temporary, and you then returned to your previous main, primary home in SC, then you would file a non-resident NY return (if you have a NY tax obligation), and a resident SC return.
NY taxes non-residents only on NY-source income, such as earnings from work performed within NY. Your resident state of SC can tax all your income, regardless of where you earn it. You would be able to claim an "other state credit" on your SC return for any taxes you had to pay to NY, so you wouldn't be double taxed.
Using TurboTax, the sequence is Federal > Non-resident State > Resident State. Proper sequence is important so that the program can calculate and apply the "other state credit" to your home state return.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
