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Sales of inherited real estate are usually reportable on your tax return, especially if a form 1099-S is issued. There will most likely be no capital gain and therefore no tax. Any capital gain would be on the difference between what the house was worth on the date of the decedent's death (your "cost basis") and what the house sold for. Your $20,000 net proceeds, after paying off the mortgage, is not relevant. If you made any improvements, those costs would be added to your cost basis in determining the capital gain.
If you lived in the house, or had other personal use, since inheriting it, you cannot take a deduction for a loss on the sale of a residence, even a second home.
If the house was considered "investment property", (sat vacant since inheriting it), you can deduct the loss.
If you had a loss, you do not need to file a SC return. If you had a gain, you do need to file a SC nonresident return. SC only taxes about half the gain.
Did mom pass ? Were you the only person on the Deed ? Contact the expert you are paying extra for to discuss all the details of this situation ... Hal_Al's answer assumes you were the only owner after inheriting the property.