Uh, I don’t know how you think fan fiction is made, but it definitely isn’t mystically spawned from dreams by dark blood magic and eating the pages of the original work. It’s written.
Have you written a thing? >> Boom, you’re a writer.
So many people fall prey to the idea that you have to do something particularly magical or amazing to be considered a writer or even to call yourself one. You don’t. It’s as simple as writing something.
Now, I think you might be misconstruing writer and author. Unless a work of yours is published, you would go by writer. I don’t think you can legitimately publish fan fic, so I think you’d stay a writer as far as I know.
But if you published original work? >>Boom, you’re an author.