Yet another time travel conundrum...

I'm writing a bit of sci-fi and I never see anyone discuss this aspect of time travel...

Let's presume you travel back a hundred years and interact in some small way with a person from the past. This would create a split in the multiverse and you would return to a very similar (nearly identical), but different present.

My questions is, what happened to YOU in the original world? You would just completely disappear out of that world and never be heard from again. Family and friends would be like, "What the hell?"

Concurrently, you would be returning into the present of a parallel world where another "YOU" presumable already exists. Kind of like Primer.

So once you begin time traveling you will always be a wanderer. Never able to get back to your original universe, you would be forced to take up home in an identical "YOU"'s world. Of course you would probably have to avoid that other YOU or keep time traveling until you pop into a universe where another YOU doesn't exist and you can fully inhabit that world as your own. But then you'd always be a stranger there too. Someone who's from nowhere with no parents. Is this making sense to anyone? Thoughts?