Painful sore throat and cough. What do I do?

For the next few hours try gargling hot/warm water (DO NOT DO IT SO HOT IT BURNS YOU), this might kill some bacteria. Also try throat lozenges. If that doesn't workout, call your doctor. This could be strep throat, but with no fever makes it unlikely. There are a bunch of ailments with these symptoms, so consulting a doctor is the only sure way to find out.