When I was a kid I used to get nose bleeds ALL the time. The doctor used some sort of chemical cauterization, a piece of gauze pad soaked in 'something' that he rolled up and put into my nostrils. I had to repeat at home for 2-3 days, and then never had the problem again. I only had to keep the gauze in for about 30 minutes at a time, 3-4 times a day. Absolutely painless, and solved the problem.