Open Question: There was a piece of skin caught on my tampon so I cut it. Bad?

When I went to remove my tampon I COULD NOT and when I went to look at it in the mirror there seemed to be a piece of skin looped around it. I tried moving it to the side but it just did not seem possible so I cut it. I cut the little flap of skin and it was painless and I removed the tampon but now I'm scared. Did I just cut something that shouldn't be cut? It kind of looks like the two end of the skin I cut are just now hanging inside my vagina. Please help. Is this okay?