There are many different degrees of collapsed trachea. I believe that, because of the devastating effects it can have, people tend to overreact to any cough a pup has. I have had a few pups with collapsed trachea and there is no cookie cutter way to treat them since they vary so much. It comes down to trial and error in terms of the meds used. The common things to do are to keep the pup in a calm environment, keep them cool and keep their weight within normal range.
To get an accurate diagnosis, a flouroscopy should be done. Of course, sometimes it can be diagnosed by manual manipulation of the neck by the trachea or by xrays but that is not 100% as the flouroscopy is.
Some accurate information is found here:
https://www.acvs.org/small-animal/tracheal-collapse