Obs cops, it does sound like your symptoms are relatively "mild," in terms of frequency, symptoms and severity.
Perhaps you could impress on your GP the importance of getting the diagnosis correct. As far as I Know, mild asthma shouldn't preclude a career in commercial aviation, but unfortunately, I aint an expert.
Perhaps he could label your symptoms, rather than your diagnosis, at this stage in his investigations. I wonder if a simple inhaler may help with your problem, prior to investigations?
Have a word with your practice nurse, they're perhaps a little more adept at managing problems simillar to yours, and they'll certainly be able to help with the diagnosis.
ps the treatments for conditions such as yours are very effective.