Sounds like kennel cough. Your vet might give antibiotics for it. My vet doesn't unless the dog is very old, very young or otherwise unhealthy. For a healthy dog, kennel cough is basically like a human cold and you can't do much except let it run it's course. Takes about 10 days. It is highly contagious. Don't let him around any other dogs!!! It's an airborne virus and can travel a long way! Keep him as quiet as possible; exercise will make him cough more.

If the coughing is distressing him, you can give a plain cough suppressant. Ask your pharmacist for one that treats nothing but coughing. The multi-symptom formulas are not safe for dogs. Not sure about the doseage anymore; it's been several years since we had kennel cough, but I think I gave my 50 pound dogs 2 teaspoons of medicine at night.