To rip off a line from Dean Wesley Smith - a writer is a person who writes, an author is a person who has written. It's that simple. If you are working on a story, if you just finished a story and are going to start a new one soon, if you are putting butt to chair and producing, you are a writer.
Please, for the love of all that is good and true, believe in yourself. Support yourself. Give yourself permission to be what you want to be. Don't be modest, don't be insecure, don't be phony. Stick with the facts. If you write, you are a writer.
You may be a new writer, a beginning writer, and so on. You are not a aspiring writer. You are not a wanna-be writer. Unless you are not actually writing. Simple.
It doesn't matter how many publishing credits you have, if any. It doesn't matter if you've been on bestseller lists, or won awards. It doesn't matter what critics, any critic, even your own internal critic, think of your work. This is a binary attribute. Any level counts. If you write, you are a writer. Be a writer, then. Own it. Believe it.
Be proud. The majority of people who want to write, never do. The majority of people who actually try writing, never even finish their first story. The majority of first time novelists never finish their novel. The majority of novelists who do complete an MS, published or not, only write one, or maybe two or three at most, novels. Every time you accomplish another goal, finish another work, you are beating the odds.
You've already beaten the most important statistic, crossed the great divide. You write. You are a writer. Go you.