My daughter would get the same kind of spots that would last for months and months and then go away. They did not itch or burn. Her doctors said that it was some type of fungal disorder that could, or could not, be related to her lupus (useless information - lol). They gave her some sort of anti-biotic cream that did not help much.
With her, I noticed that when she went swimming, the spots would clear up a bit. So, she started using a dilution of water and bleach on the spots and eventually they went away and never came back.
I'm not sure if these are the same as the spots that you and your son have, but it sounds a bit similar!
Peace and Blessings