Car not running smooth

I do not feel the car running smoothly. Every time I press the gas it feels like everything is moving. A while back I got on top of a sidewalk on the driver side only, after that the problems started happening. I took it to discount tire where I recently purchased new set of tires thinking that the tires might be damage but they said everything was fine but the tires where badly aligned, it still felt the same when I left. I was thinking it might be the suspension because every time I go in a speed bump the whole car moves but It seems that the problem is coming from the driver side. That is where it usually starts moving first. I do not know what could be the problem.