I was using a small space heater and didn't think when I went to plug in my hair dryer to the same outlet. When I turned it on, the power to the outlets in the back of the house and bathroom light are now not working.
You've blown a fuse in the circuit that serves the bathroom and back rooms. You may have to get professional help if there is no obvious fuse system in your meter board.
You've probably already done this but I'll restate the obvious. Most bathrooms (and kitchens) have GFI's somewhere in the room.