Kennel cough is a virus which is common in dogs. It presents with a cough and possibly voice loss and other symptoms. You have to remember that kennel cough is viral, like a cold is to us. HOWEVER, there can be a bacterial component as well, like when our colds turn into bronchitis, and THIS is what may need antibiotics.
If he is eating well, normal activity level and just has the cough, you can wait and let it run its course.
If you see green/yellow discharge from the nose/eyes, he stops eating or is overly tired, go ahead and see your vet.
Let me know if you still have questions.
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