Answer:
Likely athletes foot. I like to soak in hot water with a small amount of bleach to kill bacteria, then rinse, lather with soap, rinse again, dry, and apply an anti-fungal cream. If your skin is broken between the toes, you should apply antibacterial cream like neosporin until it closes before switching to antifungal cream. This addresses the itchiness more than swelling. Swollen toes can be caused by gout or fractures.