So this morning I was driving my car and it started acting up.

Its a 1988 Buick Century with around 175k miles.
I just had to replace the fan motor because it was overheating about 2 weeks ago so I don't know if that has anything to do with it or not.

But anyways whenever I'm driving now the engine makes a little click and then it revs itself and jumps up 1 or 2 mph even if I'm pressing the brakes. I'm not sure how much it revs up though because there isn't a tachometer. I'd say this probably happens every 5-10 seconds.

Also whenever the car is stopped for anywhere between 5 and 20 seconds or so it shuts itself off.

Any help would be appreciated thanks!

Should be a Throttle Position Sensor and a Idle Control Module, they are both located on the Throttle Body, you can pick up both sensors for about $20 each