I have had a few pups with CT and have never had any specific tests to get a diagnosis. The only one that really will diagnose it is a flouroscopy; but a physical exam usually is all that is needed .... and many times it will show up on xray. Just know that sometimes it does not show on xray. Info on Flouroscopy:
Special Procedure: Fluoroscopy - CVM - VetMedCenter AVID, University of Minnesota
There are many different meds that can be used to treat the symptoms....and that is all they do....treat symptoms. It is all trial and error. One may not work. so you scrap that and try another...and on and on. Theophylline does sometimes help, but in my experience, it was not the best. It helps to open the air passage ways in the lungs...but if the trachea is closing up, it does not have any effect on that.
I personally found the drugs that sedate a bit were the most effective....of course the first things are keeping weight down, activity level down, stress down and a cool environment.