It sounds like you have what is known as Dry Bronchiectasis, which I am starting to believe is more common than we once thought.
If I were in your situation, I would probably ask my doctor about the possible things to help with the shortness of breath.
Assuming you are like many of us, and would prefer not to add more medication to your life, first I would ask are there breathing exercises that can be taught by a respiratory therapist to help improve my lung capacity? This of course will depend on the overall condition of your lungs, but every little bit can help.
Then, I would ask is there a "rescue" inhaler I can use when this happens?
Finally, if already using albuterol or something similar, I would ask if there is something else in the treatment arsenal. For example, I also have asthma, and in addition to nebs, I was using my rescue inhaler (an SABA) way too much and still having shortness of breath and a tight feeling. My pulmonologist switched me to a combination inhaler that was previously used primarily for COPD. It is Symbicort (a LABA/ISC) - you can read about the different kinds of inhalers here:
https://connect.mayoclinic.org/discussion/is-anyone-else-confused-about-all-those-inhalers/
If the doctor feels the steroid is contraindicated, LABA meds are also available by themselves.

Good luck with the new doctor.
Sue