If I wanted to say "I look bad like you"
Ich mich schlecht aussehen, wie dich.
I don't know if it's correct, but my doubt is what's the purpose of mich in this situation?
"Mich" has no purpose. Translated back: I me bad look, like you. (Nope)
No matter where you got it, or what your level of German is
is horrible, like Em1 says. First thing you should know, for any language, is that you have to conjugate a verb, you can't just put the infinitive in the sentence. That becomes "ich sehe aus". Aussehen is not a transitive verb, i.e. it's not like you would "aussehen" something or somebody. "Ich sehe schlecht aus" has a meaning in itself, you don't have to refer it to yourself, so the "mich" is completely unnecessary. And then the "dich" shouldn't be in the accusative either, it should be nominative: "wie du".
But IMO there's another possibility:
That would mean "I look bad, just like you".