For me, you use "me too" when you agree with a positive statement :
-I would love some chocolate
-Me too!
... and "me neither" when you agree with a negative statement:
-Bleah, I don't think chocolate is the best idea.
-Me neither !
So, in the fish case I would use "me neither" or "neither do I" to say that, like you, I don't like it.
^^