you may just need to have a new screen protector fitted to your phone. plenty of shops that fix phones provide this service when buying a screen protector from them. Hopefully this is of some help to you.
Yes, I haven't had this problem before I applied the screen protector. Fingerprints are also a lot easier to see now, and the worst part is that it's permanently applied - I've seen videos of people trying to pull it off using thin items, but the glue is too strong and the glass ends up breaking.