Feeling like the car is sliding sideways while I am driving

Has anybody experienced the feeling that the car is sliding sideways are going to tip over while you are driving? I have had that experience whenever I go around a right hand curve on the highway, and the other day I had that feeling when I went to pass a bicyclist by going into the left lane to pass him. I suddenly felt like the car was heading towards the left shoulder of the road. I was only going 35 mph at the time. I am afraid to drive on the highway now and my Neurologist says not to drive at all. I do drive around town to go get groceries and since I live in a small town I’m not worried about experiencing these feelings of tipping over. Does anyone else have these strange feelings of tipping over or sliding to One Direction or the other while you are driving? This has really affected my life as I have many doctor appointments in a bigger city 35 miles away. I live in a small rural town of 1200 people. Any specialist I could go to for a cure??