Allow me to dispel common myths.
1. You are not a writer because someone else recognizes that you are a writer. (This one is akin to the idea that if a tree falls in the forest and there's no one there to hear it, it didn't make any sound. What goofball came up with that idea, I wonder?)
2. You are not a writer only when you have published a story, poem, nonfiction work, or book. (Publishing is very nice, and we all hope to aspire to it at some point, but publishers are normal people who love good written material. Publishers are not imperial beings who appoint writers from the populace.)
3. You are a writer simply because you write. (That's the deep part.)
There's no magic or fanfare. It's a lot of hard work, many rewrites, way more rejections than acceptances, and usually not a lot in the way of cash while you're developing your craft. (We won't mention the cash later on, because it's good to stay optimistic, and writing can pay off if you're diligent and work to become skilled in your craft.)
So here's to a year of writing. Daily writing. No-matter-what writing. Writing-when-I-feel-discouraged-and-tired writing. Writing-when-no-one-but-me-likes-what-I-wrote writing. Writing-when-not-even-I-like-what-I-wrote writing.
Because if we're writing like that, then someday, the publishing part will probably take care of itself. (But even if it doesn't, you'll be glad you captured a piece of yourself that is unique only to you on that little slip of paper.)