I am no doctor so a medical is a wise choice,
But my own Asthma not sport induced (mild) never actualy had a full attack as of yet, is caused by my allergys (hayfever and cat hair and pollution), and the fact we own 3 cats dont help much....but hey ho.
I use a purple inhalor (2 puffs a day) hello sailor

and have a blue for those short of breath moments (it never gets used more than a few times a year, normaly on summer nights when i wake up out of breath/weasey when the pollen count is very high)
Funny thing is when i go abroad i dont need the inhalers or my hayfever medication, but in the UK i need my tablets all year round winter/summer.
As i said my asthma is mild and non sport releated. I dive all year round in the UK and abroad upto depths past 100m in water as cold as 4c, never had any problems.
I personely have never botherd with a medical, as i see no need for my condition. But thats just me, as far as i am concerned i dont have proper asthma but just the odd bout of weasing after stroking the cats and getting cat hair everywear. Or on summer nights when the pollen count is very high and the wife has had the window open all night. But as far as my medical records go i have asthma, just the same as the folk on dissability who cant walk more than 5 yards......go figure
ATB
Gareth