Okay, this is kind of a weird problem, and I don't know how to describe it. It's happened to me twice in my life. Basically, a strange hard substance that feels like a tooth starts to emerge from a spot on my gums. It happened the first time when I was an adolescent, on the outer side of my gums below my front lower teeth. This time, it's happened in the spot where I have a wisdom tooth lurking under my gums.

I thought that this strange tooth-like growth actually was my wisdom tooth, but it was too sharp for a tooth surface, and I could wiggle it back and forth. When I was young, I accidentally pulled out this strange object, but it's too long ago for me to remember clearly. This time, I think I broke a piece of it off, but the base of it is still in there.

Does anyone have any idea what this might be? It feels like a thin piece of a tooth, but it just grows out of my gums, below my teeth.