A/C chirping when car in gear and in motion

Whenever I first turn the AC on it makes this horrible noise like there is some kind of belt that is grinding on some kind of gear but that stops after a little while and just chirps a little bit at any fan speed. I have not determined that there is any fan speed that does not make this noise while the car is moving, though when the car is in park it does not do this noise at all. Also, there is absolutely no actual heat coming on when using the same system. I am wondering if the two are related. In 2007 I believe it received a brand new compressor for the air conditioning. I am really not sure how to proceed with this situation. Any help?