R.M.
It could have been something he has come in contact with from another child or something at school. I would try putting a cup to two of oatmeal in his bath water. Let him soak in it and see if this takes the rash away.
Have you changed detergent, or fabric softener, he may be sensitive where the others are not. Or if something was changed in his lunch. Think over what other than detergent that he may have at that day and perhaps you may find the solution. Again I would use the oatmeal bath, its amazing how it works. Good luck and I hope he gets back with his little friends at school. I would only put cotton clothing on him for now, something loose. As well ask the school if any other children have had a break out. It almost sounds like a heat rash to me, you have explained areas' that sweat would be. Try the loose clothing and the bath.