The vet can tell if a dog has CT by palpation of the trachea. Usually it will make the dog cough when they do that. Xrays can be done, but they do not always show if there is CT. My Maxwell had CT and it showed on xray ... a couple of years after that diagnosis, he had to have surgery at A&M. I informed them of the CT because I was concerned about the anesthesia. They did an xray and said that the CT was not that bad. He nearly died after the surgery and it was then that I found out that xrays can be different depending on the position of the dog during the xray.
Dogs with CT have a very obvious "honking" sound that is very different from a reverse sneeze. I will post links below to show you the difference. Usually a dog with CT will cough when excited.
Reverse sneeze:
Collapsed trachea:
Hope this helps. I have had three collapsed trachea pups. If I can help you, Jeanie, let me know.