What could cause bloody crusty sores inside nose?

Bloody crusty sore. These are caused by bacterial infection, usually staph but can be sreptococcal as well.You need to see your doctor, get a culture done . It is treated with Bactroban (mupirocin) Cream or ointment to be used locally and depending on the lesions you may need oral antibiotics. The condition is caused folliculitis.
Lots of stuff. Could be anything from allergic rhinitis to cold sores to mrsa. Start with over the counter antihistamine and nasal saline spay daily. If after a few days it's not improving go see your doctor for further evaluation.