Um… What? Memories don’t have a look, nor can anyone tell what someone’s memories are just by looking at the person. (Even mindreaders have to read minds to get that sort of information.) The first sentence can be fixed, though, by deleting who looks.
If you are going to use them as a gender-neutral third-person single pronoun, the correct reflexive form is themself, not themselves. (Yes, I’m aware that WordPress’ spellchecker doesn’t like it, but remember, there are days when WordPress’ spellchecker doesn’t recognize comma as a real word, either.)
Add a comma after fetch (which is not usually capitalized, but whatever) and add that after fact. (Some writers go overboard in their efforts to avoid using that at all costs, and the result is usually confusing or nonsensical writing.)
You answer the door to find someone exactly like you, down to your memories until the moment this person appeared. They introduce themself as your Fetch, and the fact that they exist means you’re about to die.
(♫ …We never knock, cause nobody’s there… ♪ Sorry: sometimes a fragment of song lyrics comes into my mind entirely unbidden, and given the number of today’s glitch post, with the fiction that number makes me think of, along with terms one could use instead of fetch to describe one’s double, well, it was perhaps inevitable… Also, my brother has lately been re-reading a series of novels about a computer nerd who just wants to find his dad — and to avoid settling down into a real, responsible-adult career like his mom wants him to — and I’m sure that’s having some effect on my thought processes, too.)