Heating/Cooling Noise

I have a 1999 Buick Park Avenue, and for some time now it has been making a very annoying squealing sound, that seems to come from somewhere in the center of the dash, near the controls and such. Although it doesn’t always make the sound, when it does it will sometimes go away after a few minutes; gets worse/louder when I turn the fan speed up; and makes the noise with either the heat or the A/C running. Any suggestions?

It sounds (no pun intended) like there is a problem with the blower for the HVAC system. It could have debris caught in it, or the bearings could be dry, or the resistors that control fan speed may be problematic. If the problem has been going on for some time, then the possibility of debris may not be valid.

Thank you very much for the suggestions! Is there a relatively simple way for me to check the bearings or the resistors? Thanks again!