I have something similar.
If I breathe in dust through my nose and there's no snot, I'll rip the cartridge thingy at the back of my nose and get a bad nosebleed.
The longest nosebleed I've ever had was about 75 minutes. It was at the start of school, so I missed the rest of the day because I had to go home C:
I never get sent home for a nosebleed, even when the classroom I am in is out of tissues. My friends still have fond memories of Russian class' "blood doodles". I wiped all or the blood onto the tip of my finger and drew with it. The teacher gave me a weird look and never asked me to turn in the paper... c: