shih tzu puppy coughing and boking

Question
I have a puppy just over a month old and he has a cough and keeps boking but nothing comes up.

Answer
It sounds like your puppy may have kennel cough.  Please go to this link  http://en.wikipedia.org/wiki/Kennel_cough  If after reading it you feel that the symptoms and signs fit your puppy you need to take him to the vet.  Even if it does not you should take him anyway their may be some other underlying problem or it may have already progressed.
If your puppy came from a pet store or a large breeder and the puppy was not vaccinated with a bordetella vaccine this is possible that it is kennel cough and he picked it up there.  He also could have picked it up from the groomers, if you took him to a commercial groomer and he had not completed his vaccinations or had not waited the full 10 days after receiving them before being out and being exposed to the public and other infected dogs.  Hope this helps.  Please let me know how things turn out