1998 Lincoln Town Car Car will not turn off

My car: 1988 Lincoln Town Car Signature has 88 thousand miles, is fuel-injected, and automatic, it is a 5L V8 and rear wheel drive. Has been well maintained/never floored, etc...

I started my car and it started making a horrible sound (rough squeak) so I immediately turned the key to turn it off.

The engine did not stop. Even when I pulled the key out in my hand. It kept running. I tried pulling every fuse and went under the hood and pulled out the ignition wires but the car did not stop.

Eventually it turned off on its own(took at least three minutes).

Then I started it again and it had no problems idling or driving (I don't know if that rules out bad or worn out pistons, connecting rod, etc...)

It did the same thing again today when I started it (horrible sound and did not turn off.)

I have not started it since.

What can this be/is it fixable/is it expensive

Thank you