How did I not know about this?
After dental work, my DD had some bleeding. The gauze compresses didn't seem to be working, so I called the dentist. She recommended dampening a teabag, folding it to fit, and having my DD bite down on it.
The bleeding stopped completely within ten minutes, and the teabag also seemed to help with the pain. It's the tannins in the tea that do this. You can also use teabags to treat minor cuts and scrapes, and you can use it on your pets too! What a wonderful discovery!