It may be that, just as it's impossible for you to be killed by yourself from the future in this type of universe, it's also impossible to create information out of nothing, so the specific scenario you described would just be impossible.

This could be a kind of conservation law - imagine that instead of a story you had a golden coin, that you receive from your future self, keep, and give back to your past self after you travel, you've added some mass to the universe, which would be impossible because of conservation of energy.