96 Corolla Rear Wheel Troubles

My School Teacher daughter has our '96 Corolla in a nearby city and reported last night that the 3 month old right rear tire was worn down to wires in spots and that the wheel moves back and forth when put on a lift. I am not a mechanic and don't want to be taken to the cleaners by one. I thought this sounded like a bearing problem, but would like some more input before I head to my friendly mechanic with the car. Any knowledge you can impart about the way in which rear wheels function these days would be helpful. Thanks Loads!

sorta funny question, but are all the lug nuts on tight? if not that, then it probably is the bearing