Your alternator did it come with a pulley installed ? Or did you have to switch the pulley from the old unit ? Is it the same alternator as the old unit? ( size , number , identifcation markings ) if not this can be your problem .
On some cars, the idler pulley {usually on the belt tensioner) can squeal. If you squirt some WD-40 or similar lubricant on the front of the bearing (engine off), and the noise goes away, it is probably the bearings in the idler pulley. If this is the case, replace the idler pulley, because the noise will come back after the lubricant gets slung out of the bearing.