Are Nosebleed and Bloodynose the same?
I have a nosebleed
I have a bloodynose
A bloody nose [two words] could be the result of a nosebleed.
It is also a collocation [I will give you a bloody nose] meaning literally that you will hit the person on the nose which will then bleed, or metaphorically that you will do something that will affect them or their business adversely.