The main problem I find with asthma is--I have trouble breathing OUT. That's what brings on the deep, roaring cough at times--the attempt of my lungs to get rid of the carbon monoxide so they can suck in AIR.
But, when I do have an asthma attack, my chest will feel very tight. I use Albuterol for those, which do make me shake for several minutes, but that goes away.
I also have a nebulizer I use 3 times a day, which does not make me shake at ALL. It's called Azmacort (triamcinolone acetonide), and it is a steroid nebulizer. NO shaking or trembling...
I would definitely tell the doctor about your breathing problems--you may need a different dosage of your meds, or some different ones. And, of course, when we have a pre-existing illness, we tend to think that any new symptoms are attributed to that. There could be something else going on that would benefit from treatment. When ou have a potentially life-threatening illness like asthma, it's always better to be safe than sorry, and to report any problems to your doctor...