Asthma sucks. i grew up with exercise and allergy induced asthma and have spent my fair share of nights in hospitals, but there are lots of ways of fixing it! From my own experience, having a great pair of lungs is key. I haven't had to use any medication in about 10 years, which is a big deal. But it takes work. if i let myself get out of shape, i'll notice that I get wheezy walking up a flight of stairs; that's my signal that i need to start running again.
Cats still ruin my day, so i just avoid them (who likes cats anyway

People who have exercise induced asthma sometimes just make the assumption that they should avoid exercise-- this is completely wrong!
Stay healthy, keep your lungs strong, and your quality of life will be just fine without using inhalers every time you walk down the street.