History is supposed to be a factual description of the past. A story may or may not be true, and it may take place in the past, present, or future. Ghost stories told around a campfire, or the fairy tales we tell children are all stories, but they don't describe facts that happened in the past so they are not history. Of course some stories may be true stories and so they may describe a part of history.
Assuming you're going to be describing factual things that happend in your life in the past, "The history of my life" and "The story of my life" would both be correct technically, but I think native English speakers would all say "The story of my life".