I don't allow my boys to be given kennel cough - it is not a necessary vaccine and can cause issues. But, if you kennel your dogs, go to the groomers, go to dog parks - then it might be considered.
KC can last for months, actually

. It can progress to pneumonia - but it doesn't sound close to that w/ what you're describing. It's something you have to wait out, watch for worsening symptoms, and give cough medicine if it progresses and/or interferes w/ sleep.