Why did my nose bleed so much as a child for just being in the sun?

Dryness. Dry air can irritate the nasal mucosa and result in bleeding in a susceptible person.
Nosebleed. Heat from the sun causes vasodilation of the blood vessel on the your septum and is likely the reason for your nose bleed. If you continue to have nosebleeds, see ENT doctors for cauterization to get rid of those offending blood vessels!