This is strictly from my experience and knowledge as a native Japanese speaker... 'jibun' means oneself (or myself, yourself, herself... depending on the context), but in some context, it has the same meaning as 'watashi'. I feel that jibun as watashi is used mostly by very masculine men... not so much by women. 'Jibun' is sometimes used as 'you' in the Kansai area in Japan.
I would stick with using 'watashi' or 'boku' (if you're a male).
oneself:
これは全部自分でやりました。I did this all by myself.
宿題は自分でやりましょう。Do your homework by yourself.
me, my:
これは自分(私)の責任です。This is my fault.
自分(私)がやります。I will do it.