Passenger side A/C blowing hot air

I had the check engine light read at AutoZone all they would say is to change the thermostat. I also had the battery and alternator tested they said the battery was bad but that they believe it is the fan clutch. I changed the battery but the problem is still there. When I come to a stop the battery gauge is fluctuating down and rpm's jump a little it is loud and rough. Once you start going it drives fine. When turning on the AC it becomes worse. And after changing the battery my AC will only blow cold air on the driver side the back and passenger is blowing hot. If it was the fan clutch would that code show up? Could this be just the thermostat? And what is going on with the AC? Please help.