key is STOP the bleeding. pack it tight OR I hope you have BloodStop. We had BloodStop on hand. powder you put onto the horn to stop the blood flow.
usually would take 1/2 if not the whole bottle.
horns will bleed ALOT
and yes absolutely painful.
if you can stop the bleeding, then no vet should be required if you keep it clean and be sure it doesn['t get infected etc. kinda the thing you need to watch cause it should just scab over and be done with it.
It depends alot on if broke off cleanly too. I've had it happen a few times, it's never a good thing. She will most likely want to have someone (vet or other knowledgeable person) remove the other horn too. In my experience a one horned goat gets hung up in fences and such twice as bad as a goat with both horns.
If you don't have Blood Stop, use some flour. Try to keep him still. Give him plenty of fresh water...might add some mother vinegar in the water for an electrolyte and immunity booster.