My faithful Saturn SL1 shakes at 65-75mph, but doesn’t at other speeds. I just replaced front tires because it was worse - would shake at any speed over 65.
Were the wheels re-balanced when the tires were installed? If not, take the car back and have that done. If it was done, it is possible that the balancing was done incorrectly, but I would suspect there are other problems with your front-end.
If you are at all mechanically inclined, there is a simple test you can try. Jack up the front end of the car, one wheel at a time. Be sure to set the parking brake and block the rear wheels, even if the car is on a flat surface.
See if each wheel moves and clunks a little when you apply pressure first left and right, and then top and bottom. If either wheel moves and clunks to hand pressure, you need to replace the ball joints.
If each wheel is solid, other parts may be worn on your front end, approaching failure. You can check all of these by way of visual inspection and manually testing for wear, by trying to move each part by hand to see if the connecting parts even a little under the pressure you are applying. I don’t recommend testing the rest of your front-end.
To do this inspection the car must also be raised, and you will need put yourself bodily under the car, so you must first be sure that the car is safely blocked against rolling and you must use mechanical jack stands to support the weight of the car. It’s dangerous and best left to a professional mechanic with alift.
If you’re unable to yourself do Kizwiki’s checks, I recommend that you get the car to a reputable chassis shop ASAP. When a vehicle gets to wobbling this badly it may no longer be safe.
How many miles? Stock size tires (185-65 14)? Stock wheels?