I need to tell you about something, can you keep it a secret? I possibly gave someone permanent nose bleeds
Oh no you didn't, come on tell me this is a bogus lie. Did you? Did you give them a nosebleed on purpose?
I accidentally punched someone in the nose.
It's not okay to hurt others. You should make sure the person is okay. It might help to think about your behavior if you are accidently causing harm to others.
It's no big deal.
Hurting people is something that is criminal. I do hope you have the decency to pay for their medical bills. This needs to be  fixed so that the person isn't so upset now.