My cat did the same thing last year ... Once it got to the point of coughing every few hours - I called the vet. He ended up having pnemonia and was severely sick. Once he got on the meds - after 7 days he was fine. But he also got the pnemonia as a result of allergies. Your cat doesn't have to be outside to get allergies. Mine is indoor too and he has them. He also had to get a cortizone shot which really helped. I'd take him to the vet immediately ... A cat SHOULD NOT cough.
