I’m late to this, but I didn’t see this mentioned outright already so I thought I’d add: The sentence is not a sentence (not unless the ellipsis is cutting off the rest of it).
“The same people I went to school with” = subject, noun phrase
“people” = extra word
“who were in the same English class as me,” = subordinate clause (or something—I don’t remember all the terms for grammatical parts of sentences—but in any case it starts with “who” and that attaches it to the description of the noun.)
“who turned out to be illiterate…” = another subordinate clause (it also starts with “who”)
So as far as the structure goes, it’s missing the verb/predicate part of the sentence.
I’ll make up a predicate phrase to better show what I mean: “The same people I went to school with, who were in the same English class as me, who turned out to be illiterate, still managed to complete the reading assignment that I forgot to do.”
(It obviously changes the meaning of the sentence, the sentence isn’t be “good” this way, but I believe it is now a complete sentence. I assume the original sentence’s intended meaning is what @janbb revised it to say.)
… As for the other part of the question, I don’t personally care whether it’s “as me” or “as I,” I think both work just fine.