I guess everyone at some stage has suffered a nosebleed. (Epistaxis). The point at which it becomes a significant medical problem will depend very much on the severity, duration and the frequency of the problem.
Serious underlying causes are rare, it may be worth having a chat with your GP about your symptoms if you are worried- he should be able to rule out any nasties pretty quickly.
Common causes include nose picking, minor local infection, hay fever and common colds, and are usually treated simply.
The first line of attack for simple nose bleeds is the application of a simple antibiotic cream 4 times a day. Cautery is usually reserved for persistent cases nowadays.
Should you report it? I guess if your symptoms are over and above that of Joe Average, then yes you probably should.
Nosebleeds which havn't responded to first aid measures after 20 minutes should be treated as a medical emergency.