I have asthma, triggers are emotions, allergies, and exercise. I was diagnosed when I was 5. With my allergies, I often can't breathe thru my nose very well. So, I breathe whatever way feels comfortable that day. My allergies and asthma have been REALLY bad this summer, it's been a hot dry one.
From what you are describing, it sounds like you are breathing in too deep for your work-out. With asthma, it's not that you can't breathe in, it's breathing back out that is the problem. For me, I really have to pay close attention to regulating my breaths and make sure that I am not breathing in too deep or not deep enough........makes it impossible for me to run outside. Too many distractions! I haven't used an inhaler in 3 years, I've just gotten that good about regulating my breathing and taking precautions for triggers. (although, this fall has been tough because of the dry summer)