As a life long asthmatic, I have tried all sorts of medications. One early learning experience was to avoid Primatene Mist, since it was (still?) epinephrine, which has all sorts of side effects best avoided. Not just my opinion but pounded into me by multiple physicians since I was a kid. I strongly suggest seeing an allergist. Once I saw one, it was night and day with treatment.
All the allergists I have seen made clear that daily use of albuterol was a sign that asthma was not controlled. However, pre-exercise use was encouraged and I found it very helpful. It did take some trialling to find the combination that works for me. My current treatment is an inhaled corticosteroid+others mix (Breztri), oral Singulair, and monthly injections of Xolair. For me, all are covered by insurance and pharma discounts. Still not inexpensive, but cheaper than a hospital stay. Initially I was hesitant to use an inhaled steroid, given past experience with oral prednisone for asthma flare ups. Most of the studies I read show it stays in the lungs. Side effects are non existent for me — much better than asthma attacks. This regimen has worked so well for me that I cannot remember the last time I used a rescue inhaler outside of pre-ride. Still keep one at the ready.
To be fair, I have been off my bike for several months due to (hopefully) unrelated heart issues, but prior to this had minimal asthma issues with the above medications. I would use albuterol before rides in the Memphis heat, but there were plenty of times I forgot to take a puff or two and had no issues. I can only think of few times I needed albuterol mid ride, and was clearly allergen related.