I would huff and puff when I tried to play soccer. I'm a firm believer in specialists because they studied more in that area of medicine. I have recently been having a lot of asthma problems and also got a chest x-ray. Your son may not have allergies and thus not need the Claritin, but that is for a doctor to determine after testing. The inhaler he is taking may just be the wrong one for him.
Different inhalers work in different ways.
That is also for a specialist to determine. You are right to be concerned about your son. Until you or someone get him to a doctor, something that helps me breath, in addition to the inhaler, when I'm having an attack, is to put my arms above my head. It expands your lungs and makes it easier to breathe. Also encourage him to try to breathe slowly and deeply so he doesn't hyperventilate.