Asthma can be triggered by allergies. Oddly enough, I have acid reflux, I have severe asthma and I can't help you because I am on too much morphine for my back pain.
Acid reflux, what are you taking for it? Mylanta is cheap and good. The pulmonary doctor can really straighten you out (I hope).
Albuterol can make most people shakey. It opens up the airways...there is always a specific word for these things...avioli or something like that.
Acid reflux can cause some VERY BAD things. Take care of it. I am 60 and was pretty normal until recently, then the wheels seem to fall off.
Flovent is one of the very few meds I have not taken. I have, at my peak
about 6 months ago, been on 23-25 prescriptions at one time. about 12 were
for Asthma.
Ask for a Peak Flow Meter. Most dr. have a box full of them, free. I have 2.
At the dr. office I could hit 500-550 at peak. Same at home.
The Pulmonologist may schedule you for a series of tests. They are not painful.
After ALL my testing, I am asthmatic and I have sleep apnea. The doctor will probably schedule you for a sleep study.
Last thing...the dr. may give you the allergy test where they do skin pricks
and so on. I hated it, but it really was necessary.

I am allergic to everything now...chuckle.
Good luck, let us know how it goes......