96 Z24 Auto Tranny Pulls

I'm new but I have looked through many pages to find a problem like this. I have a 96 Z24 automatic with the 2.4 L. When I am going about 45 miles an hour and step on the gas to pass or accelerate the car pulls hard to the right, then when I let off and it downshifts it pulls back to the left. I have reved the engine while looking in the engine compartment and it does the normal rocking but nothing seems loose. The car also does not pull hard one way or the other when braking so I don't think that is the problem. Could it be a half shaft (axle), or a wheel bearing?
Thanks for helping,
Kerry

Problem solved. I started by relpacing the lower engine mount (dog bone) and that helped a little. Then I put the car on stands to find anything that could be loose. It turns out that the lower control arm on the right hand side had some play in it. I removed it and replaced both the bushings and the sway bar link and the problem is solved. The previous owner must have been hit in the right side and it threw the bushings out of wack and caused them to deteriorate. Thanks for all the help.