My puppy also has what could be the beginnings of collapse trachea. She has been coughing since I got her at 3 months old and she is now 8 months old. She only coughs after drinking. I have attached a video of her cough. It's not the best since it's only one quick cough, but it is usually 2-4 quick coughs followed by a sound like she is about to throw up, but never does. The vet said it could be the beginnings of CT, but it is too early to tell.
https://www.youtube.com/watch?v=FMopfKgfu2s