The best sweet potatoes are grown in sandy, well drained soil. You may have soil that is too damp. I suggest that you brush your damaged sweet potatoes with flours of sulfur (fine powder. This will cauterize the wound and make it less likely to rot and dry out. Store them in a cool, dry place. You may want to wrap them in newspaper. On the farm, folks used to dig a partially underground potato house and fill it with fresh saw dust. It protected the potatoes from freezing and kept them dry.