“All About My Family and Me” is correct. The technical reason is that the word ‘about’, which is a preposition, takes an objective pronoun. ‘Me’ is an objective pronoun, while ‘I’ is a subjective pronoun.
In plainer language, pretend that the title of your paper was a simple sentence. It could read like this: This paper is all me. You wouldn’t say “This paper is all about I,” and you don’t say it when you change the sentence to a title and add the part about your family.