Writer. Artist. Painter. Photographer.
What makes you feel like that, like the thing you want to be?
The usual response to this is: If you want to be a writer, write, then you're a writer. (Same holds true for painting, photography, etc. I'm just going to use "writer" as my example here.) This is good advice. Writers write, so to be a writer, you should write.
I think there's more to it, though. Doing the work will help you feel like what you want to be, but there are things that you can do and be part of that can maginify that belief in yourself. Sometimes you have experiences that plunge you deep into that I AM feeling. It may be for just a moment, but for that little space of time you feel your writerliness down to your bones.
One of these experiences happened for me several years ago. I had the wonderful good fortune to get in on a writing workshop led by Charles de Lint, my favorite author. It was a small workshop, only fifteen of us. And we sat at a table all together and talked about writing and fantasy stories and characters, and later we talked about the business of being a writer. And we spent some time writing and then read our works aloud and Mr. de Lint gave us feedback. And I floated out of there on a cloud, and I knew-- KNEW --that I am a writer. I felt it! I lose that feeling sometimes, but remembering this experience helps me bring it back.
Other things that help me grab hold of that feeling--writing in a coffee shop (actually writing, especially on a story, and not just free writing and not planning or character work or any of that); attending writing conferences; talking shop (plotting, characters, all of that) with a small group of active writers.
So my recommendation? Do your thing, of course. Write, paint, shoot, bake, knit, whatever it is. But also seek out experiences that feel to you like what a "real" writer would do, and do as many of those things as you can. Build up that feeling in yourself of I AM. Carry it with you to help you ride through the dry spells that come to all of us. Take it out into the world and let everyone know what you are.