I don't know if this will fix your problem, but put your bike up on its center stand and make sure that the notches for your rear wheel on the frame are aligned on both sides and everything is tight and even with the chain adjusters back there. I would also check the teeth on your sprocket to make sure the they are all in good condition. Along with the normal lubing of your chain & see if that helps. If not have someone ride next to you and see if they notice anything. It sounds like something is lose, but I don't think just because the wheel isn't moving side to side rules out that your bearings could be on the way out.
