Steering steers off when I run over a bump

I have a feeling that my car needs alignment but I'm still a bit concern that there could still be a problem with other components around the wheels. I purchased the car from a private owner. He told me that the car skid sideways during winter fall few weeks ago. It has some damage at the passenger side front bumper and some a little bit of a bent around the outside rim at the driver side. Now the car still runs and no signs of clicking noise or loose joints and bearings. My only concern is that when I'm driving on the road and hit some bumps and potholes. It feels like my steering kinda throws the balanced off. It feels like the rear of the vehicle goes the other way and the front goes to the opposite way. Any idea where I can start inspecting the vehicle or what you might think problem is? Greatly appreciated!