Shaking 2000 Mercury Sable

My car started shaking badly side to side while driving about 50 miles per hour. It got worse once I stopped at the light. I thought I had a flat but realized I didn’t once I stopped

I am going to say that you need to check all the wheel lug nuts first. If they are not loose then it is tow truck time because this sounds dangerous and needs a good shop to look at your vehicle.