J.
My son has this problem. His nosebleeds now are more normal, dry-air bleeds and they last just a few minutes (and he knows how to cope with them.) But when he had the problem of nosebleeds that lasted for 10 minutes, the culprit was one vein in his nose. We had it lasered by his ENT, which stopped those long, heavy bleeds that made his teachers and caretakers nervous!
Anyway, he still has the short bleeding episodes every once in a while in the winter (MUCH less often - maybe once a month.) I'd see if you can get an appointment for someone to look at it, especially if the bleed seems to be from the same nostril. Our pediatrician was able to tell by looking which vein was causing the problem, and he referred us.
We have had good luck preventatively by keeping the room humidified and swabbing the inside of the nostrils with a bit of Aquaphor at night (vaseline would probably work too) to prevent skin dryness.