An interesting and difficult question to answer. I had life-threatening asthma as a child, and as an adult it disappeared, only to flare later in adult life, then to go away again, then to reappear after a lung infection. One thing to keep in mind. If you have every had a bad asthmatic attack always keep an emergency inhaler handy. The highest mortality is among those who rarely if ever have a severe attack, because they have no emergency inhaler available.
How old were you when you were diagnosed? Do you still have trouble breathing when you breathe?
Because here's the thing: just because you're wheezing doesn't mean you're having difficulty breathing. Difficulty breathing is a much more serious episode than mild wheezing. So yes, I think you have to take this seriously, unless you like things like ambulance rides and intravenous corticosteroids.
Asthma can change over time, and it can be exercise induced. I would urge you to see an asthma specialist and tell him or her what you've said here. They can sort it out pretty easily, and probably there are things you can do to keep from having problems when you exercise. Good luck!
It depends on your physical condition. But it is always safe to assure that nothing goes wrong. Check on your physical conditions again. Asthma should be cured with proper medications avoiding the intake of steroids. You can also opt for ayurvedic medicines.
check on this blog to know the treatments offered in ayurveda for asthma
http://www.superbeing.in/blog/ayurveda-has-effective-solutions-all-your-asthma-problems/