Nother is not really a word, but is used informally and only should be used in speech, if at all. We understand what a person means when they say something like, “It was a whole nother thing.” That may work in conversation, but not in writing or any kind of formal communication. In that case, “It was a whole other thing” is what is needed.
Most of us have figured out that the word nother comes from another (with the drop of the first letter), and that another comes from adding an to other. But sometimes when another word wants to make its way into the expression, we rightly say a, but then add the dropped n to other. It seems the n sound just wants to connect with other so much that it insists on connecting itself where it doesn’t belong.
Everyone knows what a person means when they say nother, but we shouldn’t write it down. And really, it makes us sound smarter if we never say it either.