Play in rear wheel when I push or pull on it. Hub? Control Arm?

My car was parked and someone hit the left rear of 99 Deville which in turn knocked the left side of the rear bumber loose. So I quickly inspect the car and see no major damage besides the fact the left side of the bumber is hanging down (where it wraps around towards the wheel). so I rig the bumber up to be off the ground so I can drive it. The only marks (paint rubbings) from the collision were right on the corner of the car, not more than an couple inches onto the rear and side of the car from that corner. The only thing that was cracked or broken was plastic in the wheel well which was connected the bumber, which caused it to hang down. Any way this is besides the point, im just tring to give description of what has happened. My tail light was not broken although that seems to be the point of impact since there were no makings, dings, dents ect other then right on that corner. Finally getting to the point, I also notice that the right rear tire is low on air and was pretty close to the curb - pretty much touching it. This is the opposite side of where I was hit so I didnt think anything of it. So I drive off to fill that tire up and I notice a slight vibration and low humming. The nearest place to get air is only 3 blocks away so I pull up and start adding air. But come to my surprise I can move the wheel around slightly when I push or pull on it. So what im trying to ask is what could be the issue here. If I take the wheel off I dont see any damage, nothing looks bent, broken, or out of place. I try and move things around like I did with the tire when I pushed and pulled on it at the gas station. But nothing seems loose or moved around. I hope what im trying to say is understood and if I left any details out that would help let me know. I would really appreciate any help. My guess is when the car was hit the tire was slammed against the curb causing something to happen.