My RCA changes channels on its own and shuts on and off by itself, how can I fix this problem on my own?

First step would be to power off the Circuit Breaker for this circuit. Make sure the outlet is dead with either a AC Meter or a neon tester.

After making sure the outlet is off, pull the outlet and check for several things. Aluminum wiring, Loose connections, melting or charred insulation or burn marks. If you find just a loose connection, tighten it up. If you have copper wiring you should be fine.

However, if you have Aluminum wiring, and you find any of the above conditions you really should call an electrician. Houses wired with the older level of Aluminum is subject to loose connections because of the expansion and contraction properties of Aluminum. Current level of Aluminum is fine.

Old Aluminum can and very often does lead to house fires. At a minimum, the outlet should be changed to an AL/CO type outlet. That's only a very short term fix. An Electrical Inspector or Electrician can tell you for sure if you have potential problems and how they can be fixed.

Pull batteries from remote control to eleminate that possibility, you may have some dust or debris on TV circuit board.