Here is the Wiki information on the CT- It might help you-
Tracheal collapse - Wikipedia, the free encyclopedia
Maybe if you are concerned to take him in and get an Xray? Sounds the Vet wasn’t too concerned with it being CT. Maybe he is just allergic to your boyfriend’s cigarette smoke, since your Bf smokes he would obviously have the smoke smell on him..
Also make sure when walking you are using a harness and not a collar to walk him around. You never want any pressure on the trachea.