what about the skin under the beak?

by Anna
(Vancouver, British Columbia, Canada)

the skin under the beak that connects the beak, is it very shallow? what are the chances of infection if cut? is it an emergency if it is cut?

my birds have fought before and have cut themselves on the skin around their noses, but it healed really quickly and they showed no signs of irritation.

today one of my birds got the curved edge that's connected to skin on their lower beak caught on something and it bled. it isn't bleeding heavily, but they're so small (st. thomas conure). i want to bring her to the vet, but my dad won't let me. so is there anything i can do at home? i keep an eye on her just in case signs of sickness show up and then i'll have reason to bring her to the vet (dad can't argue), but i'm just very afraid at the moment.