I'm just throwing this out there - I was diagnosed with asthma at 9-years-old. I had all the PFT's, testing, and was on a crazy amount of asthma medication. When I went to nursing school, I was learning that my symptoms and signs were slightly different than most asthmatics. My clues were that the medications I was using were not helping that much, and I bought a pulse oximeter to measure my oxygen levels when I was having breathing difficulty.
It's true that sats dropping is a later sign. However, I went to my asthma doctor and explained my findings - all the same symptoms that you are having. It turns out that I have something called paroxysmal vocal cord dysfunction. It has all the same triggers as asthma, very similar symptoms, but is VERY different with VERY different treatments. Ask your pulmonologist about a test called a methacholine challenge. I am currently a registered nurse and writing a book about my experience.
My life has completely changed.
This may not be what you have, but I encourage you to at least bring it up.