Here is an article I found for you. Have a read and see what applies to your pup. From what I read I think it is just a case of waiting till he gets over it, but I don't know how long he has been suffering and what conditions he born into. I guess you will have to make that dessison. If you have any concerns I think you should contact your vet again.
Good Luck!

Kennel Cough
(Infectious Tracheobronchitis)
What is it?
Kennel cough is a bronchitis characterized by a harsh, hacking cough which most people describe as sounding like “something stuck in my dog’s throat.” It is analogous to a chest cold for humans and is only a serious condition in special circumstances (see below); in general, it resolves on its own.
How Does Infection Occur?
The normal respiratory tract has substantial safeguards against invading infectious agents.
The most important of these is probably what is called the mucociliary escalator. This safeguard consists of tiny hairlike structures called cilia, which protrude from the cells lining the respiratory tract, and a coat of mucus over them. The cilia beat in a coordinated fashion. Debris, including infectious agents, get trapped in the sticky mucus and the cilia move the mucus upward towards the throat where the collection of debris and mucus may be coughed up and/or swallowed.
The mucociliary escalator is damaged by the following:
• shipping stress
• crowding stress
• heavy dust exposure
• cigarette smoke exposure
• infectious agents (viruses such as reovirus, adenovirus, parainfluenza virus, and even the distemper virus can be initiating infections)
• Cold temperature
• Poor ventilation
Without this protective mechanism, invading bacteria, especially Bordetella bronchiseptica may simply march down the airways unimpeded.
Bordetella bronchiseptica has some tricks of its own as well:
• It is able to bind directly to cilia, rendering them unable to move within 3 hours of contact.
• It secretes substances that disable the immune cells normally responsible for consuming and destroying bacteria.
Because it is common for Bordetella to be accompanied by at least one other infections agent (such as one of the viruses listed above), kennel cough is actually a complex of infections rather than infection by one agent.
Classically, dogs get infected when they are kept in a crowded situation with poor air circulation but lots of warm air (i.e., a boarding kennel, vaccination clinic, obedience class, local park, animal shelter, animal hospital waiting room, or grooming parlor). In reality, most causes of coughing that begin acutely in the dog are due to infectious causes and usually represent some form of kennel cough.
THE INCUBATION PERIOD IS 2 TO 14 DAYS
How is it treated?
Although most cases will go away on their own, we like to think we can hasten recovery with antiboitics to directly kill the Bordetella organism. Alternatively, kennel cough may be treated with cough suppresants to provide comfort during natural recovery. Or antibiotics and cough suppresants can be combined.