Years ago, I struggled to define myself as a writer. I had a column in a local magazine, and I was working on a short story and a book, but I still felt like I was just playing around. I didn't feel like I was really a writer. When I shared these worries with a friend, her reply was simple and to the point.
A writer writes.
And that was it. As long as I keep writing - books, plays, short stories, essays - than I am a writer.