I Was Munching On Some Dispensed Crushed Ice (not Because

I was munching on some dispensed crushed ice (not because of a deficiency) and a piece cut a small gouge in my gums about a centimeter or so behind my two maxillary central incisors. It bled for about an hour after the rest of the cup of ice (about 3/4 of a glass) was held against the wound. It's finally stopped bleeding, but I now have a flap of skin about two to three millimeters long and maybe 1 millimeter wide which opens up towards the back of my mouth. I'm pretty sure I shouldn't need any stitches, but I'm not sure if I should visit a dentist or, since it's Saturday afternoon, a hospital to have that flap of skin removed, or if I should just wait it out. I realize I should have probably visited one of the two medical facilities after ten minutes of it severely bleeding, but I had no way to get there without having to take my two young boys with me. I've had ice cut into my gums before, but never leaving a flap of skin and never having the bleeding continue more than 2 minutes, tops.