Over heating A.C. overcharged dead battery

2006 Equinox the other day the relay for my air conditioner fan went out and I had to replace it I also charged the AC system however the gauge was inconsistent as I was charging using Freon from auto parts store the next week the vehicle started to overheat and I noticed that this was only happening when the AC was running as I was diagnosing the problem and revving the engine the AC compressor discharged quite a bit of freon ran fine for a day started to overheat a little bit the next day wife parked it turned it off and said that the fans continue to run for more than a half-hour I believe the battery is now dead any ideas or suggestions?