My view and I have pretty much the same condition as yourself is to let your AME find it. Ie so long as you test ok during each medical then I wouldn't divulge the info. After all, you're not "asthmatic" as such. Remember, people can hold class 1's with asthma, it just has to be effectively managed. It sounds like you're a long way from being medically threatened with asthma.
So long as you now have it treated effectively when it's active you'll probably find the rate of coughing decreases. You can ask your local doctor if s/he feels it ought to be reported. Personally (and I am not a doctor) I think not.