An outlet on the wall next to where my air conditioner is plugged into is hot to the touch. I have nothing plugged into this outlet. Why would this happen. It only happens when the air conditoner is running.

The connections ar probably loose. Loose connections generate Heat.
Turn off power to AC, If You understand Electrical, and the risk, Remove receptacle, and secure connections. Pigtail and do not use push in, use screws.
More than likely power goes to "hot" receptacle, then to AC. Own circuit would be better.

I also suspect the outlet that is hot will need to be replaced with a new device as the loose connections probably damaged the back of the device.