Yes, TurboTax can handle this common situation. You'll be filing both a non-resident NC tax return and your home state SC tax return. In the Personal Info section of TT, enter SC as your State of Residence, and indicate that you had Other State Income from NC. This will prompt the program to generate the correct tax forms.
You must then complete the non-resident NC tax return first, before you do your home state return. SC will grant you a credit for the taxes paid to NC, so you won't be double-taxed.