My thought is that your son probably does have asthma
(incidentally, RAD is basically asthma
...they just don't like to call it asthma
until it's been chronic). He is probably sensitive to the chlorine or other chemicals in the water.
Also, if he's anything like my son, he has a lot of trouble with colds turning into infections and usually pneumonia.
I would take him to either another asthma Dr. and explain the pool thing to him/her.