Re: could my son have asthma?
No - it's not normal for kids to wheeze. Turning red - maybe. My son was finally diagnosed 2 years ago at age 5. Most of his was breathing issues were considered "exercise-induced asthma" (probably what your son is doing now). Now my son is on a preventive everyday asthma medicine. I wish he could have been diagnosed earlier. The earlier a diagnosis - most of the damage is reversible. Luckily so far - every time he gets bad - we get on it quick - and he comes out of it after a week or so. Luckily no hospitizations, just a couple ER trips.
Please get your son checked - he should always have a rescue inhaler around when he exercises. My nephew who has this actually takes a couple puffs before any sport and then he doesn't need it again. Whereas before he would have the same trouble as your son.
Best of luck to you!