M.P.
You need to get your son to a pediatric allergist immediately. Sounds like your pediatrician is not at all equipt to deal with asthma. Many are not. I noticed a huge difference in the asthma care from the allergist than from our ped.
First of all-it sounds like your son should be on pulmicort. You use it through the nebulizer once or twice a day. It is a long term anti inflammatory that puts the lungs in a good condition. Even though there is a bit of steroids it is 100% better than the huge dose that you are giving him with flareups-and Pulicort will help prevent the flareups.
You also need him to get allergy tested. My son's asthma symptoms were made much worse by his allergies that we had no idea that he had until testing. He didn't get the classic symptoms as much so we didn't know. Turned out he is allergic to everythng outdoors and most things indoors. We give him zyrtec every night and it really helps. He is practically sympotm free now at age 7 and has not had an asthma attack in ages. I believe that this is a combination of good asthma care and outgrowing it.
But do see a pediatric allergist.