I would guess that either your A/C compressor is seizing up or that your belt is dry and worn. Check your belt for cracks on the side that contacts the compressor pulley, and make sure it is tight. If it looks like it is in good condition and tight, you can get "belt dressing" that makes the belt a little tacky so that it doesn't slip, but I would just replace it and make sure it's tight. If the squealing continues you need to have the compressor looked at or replaced, if you want to run the A/C.
