Hi, Milva
I think that when "wrong" is referred to a person, it can only mean "not right", "mistaken"...
Then "wrong" can also be used in a lot of different ways when it is used in idioms (like "What's wrong with you", etc.)
Your sentence is strange, I mean, I don't understand exaclty... As you say, it seems the girl has made or is making a mistake in some way. It would make sense if it was:
You think you make me feel like a fool for being alive, child, but you are so wrong! (you think you do, but you don't)
or:
You make me feel like a fool for being alive, child, and that's so wrong! (different meaning = not morally right)
These are just my thoughts, I might well be wrong.