My dog had a problem like this, got to the point where she couldn't even play outside, as soon as she would try to run she would start kind of coughing/sneezing. Found out she was allergic to a cat we had brought home shortly before she started acting this way. It started with a cough, turned into coughing fits, asthma type reaction. She is fine now, had to get rid of the cat.
When I took her to the vet they did check her trachea, it was fine, and they were going to test her heart next. Boxers are known for heart problems. But it ended up being the cat