自己~=self~
自己紹介self-introduction 自己実現self-actualization 自己批判self-criticism
~自身=~'s self
彼自身himself あなた自身yourself 山田さん自身Yamadasan's him/herself
自己 and 自身can mean "one's own self" as itself.
For this meaning, 自分is more casual, colloquial, ordinal word, whereas 自己 and 自身 are more formal, academic, and somewhat sophisticated term.