I also have asthma and that's what it sounds like to me. I would see a doctor to be sure though. There are many triggers, exercise, allergens, etc. I have all of them. Mine was adult onset also as I never had asthma (that I'm aware of) as a child. I carry my inhaler with me at all times! I also let ride leaders etc be aware that I am asthmatic and have medication with me. Hot days are a REALLY bad time for me. Humidity is rough as well and here in Indiana we usually have BOTH during the summer.
Good luck and keep us updated to what you find out. If you do in fact have asthma, you'll likely be given an albuterol inhaler (rescue inhaler) and some sort of inhaled steroidal preventative medication.