Sorry you are having a bad week.

"Kennel Cough" is a generic term for an undiagnosed upper respiratory infection. There is no one virus or bacteria called "kennel cough"; it is a syndrome, a cluster of various virus and bacterial components.

Depending on the strains the dog has caught, antibiotics often can and do work very well - if the version of "kennel cough" the dog has caught contains bacteria. If the main component happens to be viral, such as the common bordatella virus, antibiotics will not kill the virus, obviously, but often prevent the dog from developing secondary bacterial infections and/or pneumonia, thus shortening the length of even a viral "kennel cough" battle.

I agree, however, these symptoms do not sound like "kennel cough". "Kennel cough" is most often simply a loud, seal-like cough.