Peeling skin can happen for a number of reasons. One other mom mentioned a strep infection and that's true, strep can cause your skin to peel. You can also get skin peeling with the hand, foot and mouth virus but that should be temporary just like the step. For people who have long term peeling, that's usually a sign of an over abundance of yeast inside the body. This is something we have to attack through diet and by building gut flora.
You can also get peeling with some medications but those three are the most common reasons. If you get a negative strep test and he doesn't have hand, food, mouth, I'd treat for yeast because the treatment does no harm whether he has it or not. And, if he does have yeast, you'll see the peeling improve. Unfortunatly there's not a simple test to see if he has a yeast overgrowth. His response to diet and building gut flora is your best test.
Let me know if I can help, I see patients all day who have yeast. It's very, very common but usually goes untreated because it presents as an unusual combination of symptoms and is different from person to person. But, I will say for people who feel they have an addiction to sugar or refined carbs, that's a good indicator.