If you can rev the engine, then I would suspect the engine is OK and that the transmission or transmission linkage is the culpert responsible for your not being able to move. I’m presuming this is an automatic.
I am, however, puzzled by your earlier statement about the car accelerating on its own. Can you elaborate? Are you simply experiencing “fast idle” with a cold engine, since you had driven less than a mile? Or was it something more dramatic?