AC Compressor Pulley?

First off, its the 2005 pontiac sunfire. The air is cold as long as your moving, when idling however the air stops running cold and the rpm will get really low and jump back to normal until you accelerate. Of course it doesnt do this with the air turned off. I was thinking the clutch on the ac compressor was going out and this would be the cause of the quick, weird belt noise once I do accelerate. Of course I got the, charge the a/c bit and maybe the low freon is causing the clutch to always be engaged. But Im not charging the damn thing if its ice cold when Im moving and not knowing if thats the real issue