How can I get the light cover off my fixture?
There are fixtures now that screw in like a bulb over an keyless socket or similar. Turn the whole thing gently and see if it unscrews.  

For example 



https://www.homedepot.com/p/Commercial-Electric-Lightbulb-Replacement-Fixture-7-in-Round-White-60-Watt-Equivalent-Integrated-LED-Flushmount-Bright-White-54483142/205890895