Hi Jonnyturkey,
If I had a chest X-ray or CT scan at the height of an asthma problem (unless I had pneumonia), it would not show a problem. The best test of lung issues/breathing tightness, is a peak flow meter (Spirometry--, which you'd find at a pulmonologist's or asthma doc's office.
en.wikipedia.org/wiki/Spirometry)
You may not have any lung involvement, but from my experience, and the experience of many others here, have found that their lung issues are caused by some amount of acid or acid spray getting into their lungs.
Once you're on treatment, and the acid is suppressed, it will take a while for the lungs to heal. You should see improvement, though. If you continue to experience breathing issues, you should definitely have it checked out by a pulmonologist.
Good luck!
Denise