2002 Chevy Cavalier trouble, revs up and down?

I have an '02 Chevy Cavalier that wants to rev up and down whenever the air conditioner is turned on. A lot, by more than 1000 rpm. It also does it when the fan is turned on, but nowhere near as badly. It's also worse when stopped at a red light, the engine is audibly revving up and down, and I can even feel the car lurching forward and backward. It's hardly detectable excluding the above. Can someone tell me what is wrong, why it's happening, if I'm at risk of breaking down mid trip, and how to fix it? Thanks in advance!