Your IAC (Idle Air Control) valve is getting old and cranky. Time for a new one, probably.
Turn your climate control to OFF and see if the problem goes away. The IAC is supposed to compensate for the extra load that the A/C compressor places on the engine when the compressor clutch engages so some increase in idle speed is normal. Sounds like your IAC may be overshooting.
Before replacing anything, do check your A/C system for proper charge. It sounds like it is short-cycling and may be contributing you your symptoms.
The IAC has very little effect on intake air above 20 mph.
Steve