Why do I owe S.C. taxes & I didn’t work in S.C.? Just live in S.C.

In general, nonresident pay income tax on state source income, which includes wages for working in the nonresident state.  You must report and pay income taxes to your resident state.  You can claim a credit for taxes paid to another jurisdiction for the taxes paid to your nonresident state, so you will not be taxes twice on the same income at the state level.  

@Ashlibrigman36 you file a NC non-residential tax return AND a SC residential tax return.

SC will give you a credit of the LESSER OF a) the tax you paid NC or b) what you would have paid SC had the work occurred in SC.  That way you are not taxed on the same dollar of income in both states.