Instead of saying, "Did you come here yesterday, too?", can you say, (1) "Did you, too?" and (2) "So did you?"?
The simple answer: you can say (1), but you can't say (2).
It is true that the word "so" can mean "also". (For example, if someone says "I saw a penguin yesterday", you can say "So did I!", meaning "I did, also!") But (with a caveat) the word "so" can't mean "also" in a question like (2).
I don't know how to explain why you can't use "so" in that way. I think it's because the word "so", when used to mean "also", has to be at the beginning of the sentence or clause, but in a question similar to "Did you, too?", the head verb ("did", in this case) has to be at the beginning of the question. These two requirements contradict each other.
The question "So did you?" does make sense in a different context. For example:
"Jason said that I should go to that German restaurant."
"So did you?"
"Yes, I went there, and the food was delicious!"
But in the above question, "so" doesn't mean "also"; it means something like "consequently". (Also, the stress in the above question is on the word "did".)
Now, when I said that the word "so" can't mean "also" in a question like (2), I said that there was a caveat.
The caveat is: any sentence can be made into a question without changing the word order, as long as your intention is to ask for confirmation. In other words, you can ask "So did you?", but only if you think that the answer is yes. In this usage, the question "So did you?" is equivalent to "You did, too?", not to "Did you, too?" Also, in this usage, the stress is on the word "you".