Kennel cough sometimes takes a while to leave the system. You should see a gradual improvement over time. Just keep close watch to make sure that there's no worsening of chest congestion.
As far as meds go (cough meds, etc) I'd never give anything to my pup without first asking my vet. There are some human meds that dogs can take and there are some that are absolute no-no's. They metabolize meds differently than we do (much differently) so it's imperative that you get instructions on dosage as well.
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