I think that if indeed time travel is possible, changing the past would either:
Make the future (the time you are from) the way you remember it. You actions in the past were responsible for the outcome you remember.
Or, set the timeline onto a new track in the quantum multiverse. Your time still exists, but you will no longer be able to get there travelling through time alone.
Although the latter has complications with causality that I don't like, and may make it impossible.
Stephen Hawking postulated that going back in time would create something of a temporal feedback loop that would eventually result in the time machine never having been built, thus acting as a sort of space-time immune system.
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