It could be dryness, hair tickling, stress, broken nose or fibromyalgia. For the nose bleed you need to wipe it gently and if it doesn't stop then you need to consult a doctor. To reduce dryness, you can buy over the counter such as saline spray.
It could be dryness or a hair tickling. For dryness, you can buy a saline spray at the drug store. I just scratch my nose. I don't' get the nose bleeding sensation but it might mean your nose is running a bit. Wipe it gently.