How can I change the drawer pulls to update my kitchen?

There are a lot of reasons screws can get stuck - they can be stuck because of the paint/stain, build up, stripped, etc. Here is an article that might help you with your stubborn screws - https://thecraftsmanblog.com/4-guaranteed-tricks-to-remove-stubborn-screws/

Hi Kat, It sounds like the side you can't get to unscrew was glued in - general done by someone who didn't know how to use wood putty to fix a hole that had worn out. If that is the case, you will need to use a Saws-All - or get someone else to use it - to cut the bolt/screw off just behind the old drawer pull. This will let you remove the bolt from the inside of the drawer. Then fill any damage to the hole with wood putty, let it dry, and install the new pulls.

Hi, Kat, if you haven't yet tried this option, you can place a wide rubber band between the screw and your screwdriver, for extra friction. If the screw isn't stripped or glued in, this may work.

God you guys are cool. Thank you.

sounds like you have the part on the back of drawer out. if so, try tapping the front of the handle, it might loosen it enough to release it so it can be pulled off, or try slicing around the part that attaches to the draw front as that might release it, if neither works, read above hints.