My Phone Has A Screen Protector Made From A Type

My phone has a screen protector made from a type of glass and is cracked in some places and I cut the tip of my finger on it no less than 2 weeks ago. The cut is very small (literally a tiny dot), but it still hasn't healed. Is it possible that there is a small piece of glass in it preventing it from healing? Normally cuts like this go away pretty quickly for me. If it's not glass then why hasn't it healed?