I know all about this...we just had a kitten literally covered in it. My children were prevented from getting it and I was practically paranoid about it myself but I'm slightly immune compromised and ended up with some anyway.
I read all of the OTC ointments to see which said it would cure in 1 week. Then I bought one of those in the store brand. Instead of following the directions of putting it on once a day-I put it on every time I went in the bathroom. At night I put it on and experimented with various types of bandages until I found one that allow the air to reach through but didn't dry up the ointment too fast. What I found was most commerical bandages don't work well. Best thing was a square of toilet paper held in place with first aide tape. Hard to use in the hair though.
Along with that, I've been taking odorless Garlic capsules because garlic kills fungus. Mine cleared up quickly-I'd say in about a week and half. There's still a shiny spot where it was and the hair hasn't grown back in yet but it's not "alive" anymore. It does take a while for the skin/scalp to fully recover and in some cases, if it was REALLY bad the spot may not ever grow hair back and be like a scar. That doesn't happen often in this current day and time though.
Hope that helps. My daughter is 6 and I doubt she could swallow garlic pills like I do but I do know you can get liquid form and stir it into juice. Orange juice hides it best that way. (I've done that too in the past.) Garlic will also fight other infections and boost immunity and repel mosquitos and there are no ill effects. The odorless variety prevents us from reeking of it too which is a plus.
I wish him the best in his fight to recover!