Hmmm...sounds like kennel cough to me. Kennel cough is very common in puppies, especially ones form puppy mills.
Neither of my babies have collapsed trachea (knock on wood) but they both had kennel cough. Actually, Willow still does. When Biscuit had it as a puppy, we did the antibiotics and so on and so forth but they did not clear up the kennel cough. I thought he would never stop coughing! It really worried me, but sure enough, after a few months (which seemed like forever) it finally went away. But it did seem like it never would. We just eventually put him in a room with a humidifier at night (this is when he coughed most) to help ease his little throat, but did not put him on more than two rounds of antibiotics.
Putting them on antibiotics is understandalble if it is an acute case where the dog is lethargic or not eating etc., but for the more general case where they seem to be normal in activity and eating and seem to feel well, antibiotics should be used to prevent a secondary infection, like pneumonia. Our vet did two rounds with Biscuit, but then decided that any more rounds would not be beneficial.
Actually I have since learned that it is best to help boost their immune systems the best you can by diet and help control the cough, but to let it go away on its own. Right now, Willow's cough is worse when she plays, but I am just giving her a supplement to help boost her immune system and letting it go away on its own. Having been through it before helps, becasue now I am not always freaking out like I did the first time.
Kennel cough can be stubborn, but it will eventually go away. IMO that's what it sounds like to me, but then again, I am not a vet......
Do some research on your own, here are a few good sites to start:
http://www.peteducation.com/article....&articleid=452 http://www.icanimalcenter.org/librar...nnelCough.html
I hope that your baby does have kennel cough and it's not something more serious, that way, it will get better. Hang in there!