Infant son had kidney infection which was treated. He now has small area on his thumb and and middle finger that looked like it peeled off. What is this?

Peeling Skin. With a history of recent antibiotic therapy, it is possible this represents an allergic reaction to the antibiotic, especially if it was a penicillin derivative. As long as it doesn't appear to be getting worse or his condition remains the same, it might be a mild, self-limited reaction. As an alternative, children often get eczema in these areas, which responds to cortisone creme.