I just moved into an apartment, and there is a flush mount ceiling light fixture that I can not remove, and I need to replace the bulb.
This is an old one, the metal rim is not movable at all, but the glass acts like others said the metal ring should. The glass is also spring loaded, so the most I am able to do is get a screwdriver under it. How am I supposed to remove the glass so that I can change the bulb??

Does it have a decorative piece of metal in the center? If it does that might unscrew and allow the glass to drop down. Hold the glass while you do it because it could fall.
The metal trim may be hinged. You might be trying to pull the wrong side down. Make sure the paint isn’t sticking the trim to the ceiling. Metal should pull down, not the glass up.