In my practice, most often ear bleed happens after a slap on ear/cheek or when someone tries to clean the ear himself. If ear starts bleeding, then it is tendency of persons to put some kind of oil/fluid into ear. I discourage such practice strongly because this introduces the infection into the wound site. If ear drum is ruptured, then infections can go to middle ear and ear can start discharging.
Most of the ear bleeds stop on their own. At the earliest try to consult ENT specialist.
Nose needs no reason to bleed while the same is not true with ear bleeds. Trauma remains the most important cause of ear bleed which is often self inflicted during cleaning by the person.