NO! "still" and "yet" are not the same word. Come on, man, do a bit of self studying. The differences between the two words are very clear.

I think you cannot use "still" with a negative question like this. the question should be "are you still tired?" or "aren´t you tired yet?", these two questions have different meanings. "are you still tired?" implies that you were tired before and continue tired now. "aren´t you tired yet?" this question presumes that you were not tired before but you should be tired now.