My daughter was diagnosed around 6mths with asthma and to be fair i didnt have many troubles getting her diagnosed. I did find that a few people i talked to, had to basically bug their doctors 2-3 times a week making appointments, to force the Dr take notice. This may be what you need to try next as some Drs are extremely pushed to the limit and don't have the time to listen properly. Which results in them thinking we are paranoid mums the majority of the time.
Just to give you something positive though, my daughters was quite severe while she was a baby and toddler.. but she turned 7 on Friday and we have only had to use her inhaler twice in the last 3 years. I hope your little boy can get some relief and help soon.