At around 85 mph, the steering wheel starts shaking violently. How can I fix this?
Don’t drive 85 MPH . Also have tires balanced .
First step is to have the wheels balanced and ask them to inspect the wheels for any damage.
Second is to inspect the front suspension, especially the tie rods and tie rod ends.
If you don’t know how to do this, have a trusted alignment shop check.
The probability of excessive wear of ball joints and tie rod ends on a 22 year old car is… very high… and potentially very dangerous. Until this is rectified, I strongly suggest that the OP NOT drive his car at 85 mph.