Doctor prescribes antibiotics to cure infection .even though infection may be on finger or external?

The threat of infection is the "in" part. Moldy skin does not matter much because it's dead anyway and it falls off anyway. So you want systemic protection. They use povidone iodine to prevent surface infections.

I just recently learned about povidone iodine. They say it is superior to tincture of iodine, and much cheaper.