This is
VERY important regarding medicine...
OK, for your albuterol... are you taking your medicine at least 15 minutes *prior* to your exercise?
If you do not, trying to take it after you are already in a full blown attack will do little, to no, good. Unfortunately

...as you have already figured out.
I wear a HR. If my "wind-less-ness" is due to my HR reaching it's max... and when my HR recovers, and I can breath again... I know it was not the asthma. Hope that makes sense. If it was the asthma... you would not be able to recover when your HR came down... you would still be constricted... and could not suck wind in to breath... that would be the asthma.