Unsure about screen protector type?

I bought a preowned phone from boost mobile. Phone was absolutely great from the moment t I got it. Heck it even came with a screen protector already on it. So like any responsible owner I went and bought a case, and that's when it all went wrong. After a few days I started to notice the edges of where the screen and the case meet started to peel up. I take the case off and apply pressure to these areas and it would mostly “lay" back down. Case goes back on and then it got worse. So last night having got tired of looking at it, I attempted to remove it….. this is where I went wrong. Only the areas that were peeling broke off. I know it's some kind of glass because it cut me. I have no idea what kind of screen protector this is and now I have its glass sticking up and it won't come off! Someone please help me and tell me what to do…..thank you in advance