Build-up of dust, hair, hairspray, etc. most likely is the cause of the screeching. The easiest solution would be turn off the power to your bathroom, take the cover off your fan, and wipe it down. Also spray the blades with wd-40 or oil to allow them to rotate more fluently. This should pretty much take care of the problem, however if it persists, you should probably get a new fan, they are relatively inexpensive, but in either case, the fan should be cleaned at least once a month or so, normal household maintenance.
Tim the Toolman Tayler, April 2009