Very good possibility that you are burning your gum tissue. Think about this--if hydrogen peroxide can take the color out of your hair, what can it do to sensitive gum tissue?
Now, I have burnt myself in various ways too (I once burnt myself "down under" using a tea tree oil douche) so don't feel bad. Sometimes our Science experiments just go bad.
If your gums are not sore now, just leave them alone and maybe use a toothbaste like biotene (no floride or harsh detergents) for awhile. If your gums are sore, I would consider going to get some tri-salts (cal/mag/pot power mix) and swishing that around in your mouth a few times a day for a couple days.
As for the vaginal area I would suggest inserting a cap of good probiotics of there for a couple of days. I found that really works for me.