Staying in shape is an absolute must and the best way to stay in shape is to be active. Any kind of sport would do but from my personal experience, I would highly recommend swimming. This is especially the case if you have asthma. If you've got asthma, my number 1 recommendation would be a ton of sport and if possible, endurance training. Swimming is a great all round sport that if done correctly, will train your whole body. While I was in America, I swam competitively for about 5 years till I moved to Germany. I was on a swim team where we had 2 hours of practice every single day and competitions on weekends. It was a great experience and I had alot of fun with all my friends. If you have a choice always pick outdoor swimming and try sign up with a few friends. It'll help to make the experience more memorable.
I also played a lot of soccer, over 6 years to be exact, but I had to quit that to make time to learn German. I had a very strong kick from bicycling everyday to school so I had a decent advantage. I also played a bit of casual table tennis and also tennis for a few years just for fun.
In Germany there's a sport called handball that is very fast paced and a lot of fun. I played on a team for 3 years till the training location moved far away.
I also did quite a bit of long distance running, but I can't really recommend it at all. All I can describe it as is 100% endurance and random pain. It becomes really hard to estimate time and distances and it's just not fun compared to other sports. My record a few years back on 10 km was 41 minutes which I still I find quite astonishing. I've since gone back to bicycling.
In the past, I had really severe asthma. I was actually brought to the emergency room by ambulance on multiple occasions and had to stay multiple days. Let's just say that asthma poses a bit of a challenge, but with enough effort you can overcome it or at least suppress it somewhat.