Welcome to the forum!
Does this seem to only happen when you are using the air conditioning or defroster? Are there any other pulleys that may be seized or have bad bearings? With the belt now off, spin all the pulleys before putting the new belt on to attempt to determine if you had a bad bearing somewhere, or one that is about to fail. You probably won't be able to spin the power steering pulley easily by hand, so just check that one for play in the shaft.
-Rod