My son (now 34) had Asthma from the age of 9 months. He was prescribed inhalers which never made any difference, and he was in and out of the hospital for the first 8years of his life.
The ONLY thing that ever worked was Prednisolone tablets (corticosteroids), and in the end, my GP allowed me to always keep a supply at home, so that I could start treatment when Shaun was bad, thus avoiding trips to the hospital.
Has your son got Eczema as well? The 2 conditions often go together - my son no longer has Asthma, but his skin gets extremely bad. He uses a variety of creams (some prescribed, some bought)
With Asthma, I'd suggest avoiding triggers (pollen, fur, wool, stress, can all be triggers for some sufferers), and ask the hospital for Prednisolone.