Get the puppy into the vet as well. At 3 months he/she should be able to get his/her first Bordetella vaccine. Nothing is worse than having two dogs with Kennel Cough giving it back and forth to each other. Been there, done that and didn't sleep for a month due to all the coughing!
If it's indeed Kennel Cough, your vet should be able to give an antibiotic as well as a cough suppressant. Do not give over the counter cough medicines to your dog without discussing it with your vet first. Let us know how it goes