'I got my nose broken' is something an american person might say. English people don't speak like that unless they have been watching too many american television programmes. 'My nose was broken' is correct English. 'I broke my nose' is also correct English. It implies that you accidentally broke your own nose.

1.I got someone to break my nose deliberately 2.The same 3.I did it to myself (probably not deliberately but it is not stated if it is on purpose or not)

"I got/had my nose broken" means someone else did it for you. People usually understand that you unintentionally/accidentally broke your nose when you say "I broke my nose." but of course, it can also mean that you literally broke it yourself depending on the context too. For instance, if you are writing a scary story about witches and blood magic, you could write "The witch broke her (own) nose and let the blood slowly drip into the cauldron. She had a most vile potion to make which required blood magic." The word "own" is optional.

I see what you are thinking about here, but in fact the opposite is true. 'I had my nose broken' and 'I got my nose broken' suggest that you asked or even paid another person to do this for you. 'I broke my nose' is ok, and you would understand from the context that this wasn't intentional. If you really want to separate yourself from the event and emphasise its accidental nature, you could say: 'My nose got broken'.