Shaking 1991 Chrysler Fifth Avenue

I have a 1991 Chrysler Fifth Avenue (3.3L V6). I drove the car today and noticed the car had a slight roaring sound at highway speed-- almost as though riding on bad pavement. It has really been raining here the last two days because of the hurricane, so I thought maybe that was it – a wet surface and bad pavement. But after a few minutes, I noticed the car was shaking, and I could feel it in the steering wheel. I tried to slow down, and the car shook even more. I could accelerate with no problem, and there were times when the car seemed fine. But I did notice that at 40MPH it was particularly bumpy.

The car is old, of course, and had a transmission replacement ten years ago at 70k. It now has 130K approximately. The tires appear to be good on the front (two years old), and the car does accelerate (shift/downshift) seemingly fine. I did smell a slight burning odor (like something had gotten hot) when I parked the car at home, but with everything wet, nothing was clearly “hot.”

Any ideas? This started today after an errand of 50 miles and really shook me up (no pun intended). Do you think it could be a bad tire, wheel bearing, sticking brake (when I would brake, the car would really shake hard), something else?

Thanks for your help. It is appreciated so much!