When you say difficulty in breathing, do you mean that feeling that you sometimes get after being in a pool for a long time where if you take a deep breath, it kind of hurts your lungs?
If a person gets that feeling after any exercise, yes, it's not a bad idea to get checked for asthma. But if it only happens after swimming, I would think it much more likely that the issue is related to that pool.
Chlorine allergy is also a possibility, if the person experiences symptoms in pools that don't occur elsewhere.
I've also done some high intensity training outside of water without the same lung issues. I'll get out of breath after running for a while, but the pool related issue is every time I breathe in deep to expand my lungs, it would feel very strange and hurt. It would last even an hour after leaving the pool area.
I do think it’s strange when I see people jogging along polluted arterial roads for this reason. Especially when there are often traffic-free trails or quiet back roads available nearby!