なんて = surprise or disgust (or any feeling of the extraordinary)
「恋なんてもう信じらんない!」 = I don't believe in such a ridiculous thing as love.
なんか = expresses a strong statement to the contrary.
「私なんか、いなくなったほうがいいじゃない?」 = You wish I were dead, don't you!
I can only explain this in English. The two expressions are VERY different. In fact, you really can't confuse them.