1996 Cadillac Concours my car is shaking

Visually inspect the tires look closely at the tread area. Look for a lump or bulge. If you find a bulge, you will need to replace the tire. (Simple and most inexpensive)

While you are inspecting try and move the tire by hand. Grab the top of the tire and give a good pull, Maybe it will move or "clunk" in such case you may have a bad wheel bearing. In that case you would look at $125 in parts and two hours labor at your local repair shop.

Last: while you are inspecting. Try to twist the tire by hand, right to left. If it moves or makes a "clunk" that will get expensive fast. You maybe looking at tie rod ends, front alinement, extreme case steering box or other related componets.