Rpms going up and down and trouble shifting gears
So I have a 2003 Jaguar S-Type that has automatic and a button for standard too. The automatic side wouldn't shift gears and made a loud sound when rpms would go up and down very fast. I started using the standard side and the rpms move up and down but not as bad. Lately when in idle the car the rpms go up and down when parked. My dad checked the transmission fluid and that's fine and full. Not sure what this could be but I want this looked at and don't know where to start.