South Carolina does not have a true part-year return. Rather, they either will tax you as a nonresident or as a full-year resident. If they tax you as a full-year resident, all of your income is taxed in South Carolina, but then they give you a credit for the tax you pay in the state where you came from. This doesn't work for you, because you lived in Florida which has no state tax. Therefore, you will want to choose the Nonresident option. This way guarantees that South Carolina only taxes the income you made while working in South Carolina.
If you cannot find this option when you select the part-year resident, then start the state return over and select nonresident so that your Florida income is excluded from the South Carolina return. (One caveat: South Carolina may still pretend that all of the income is taxable, and then prorate the tax to the percentage of income earned only in South Carolina. This is still less tax than if all of the income is actually considered taxable, which is what happens when you use method 1 described above).
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