The microwave smelled like it was burning and the top on the outside felt hot. I left it unplugged for a while and when I plugged it back in it started running on its own, then started feeling hot on the top again.

Sounds like it over heated and you have some wires that might have melted and are causing this issue. In either case I would not recommend using it any more for fire hazards and would recommend you replace it. repairing these is not economical. You can unplug it and let it set over night then remove the case and see if you can find what has gone bad and decide if you need further info on a repair if you chose that route but i can't tell you what the problem is without seeing it or a better description of what is burnt.