So my baby Maximus is four months old and I got him just one month ago. From the first day he had this cough and the vet said to keep on eye on it and gave some antibiotics. Well, his cough persisted for two weeks! So she suspected that it was a collapsed trachea.
Suddenly, after two weeks - the cough disappeared! So I figured he must have had some kind of upper respiratory infection. But then this morning his cough came back! He coughs when he wakes up, and was coughing when he was eating. But after some time and during play - no coughing. Could it be a collapsed trachea?

Supposedly if it was, he'd be coughing when he's exercising.
I took a video clips of it and am linking them here. Please tell me what you think it is...He's had it for a month (including 1 week when it was gone) and I want to make sure he'll get whatever treatment he needs.
http://www-personal.umich.edu/~choin/cough/