Writers. What makes somebody a writer?

I am taking a writing class. I don't think I am a very good writer. I used to be a great writer when I was a child, but school beat it out of me and now my writing is not very good.

When I think of writers I think of people who read a lot and who read other people's writing while holding a pencil. They make little squiggly marks indicating where proper punctuation ought to go and where the grammar and phrasing is all wrong or where typos occur.

I am not like that. I have typos everywhere all the time. I don't know how to use a comma properly, let alone the difference between an endash and an emdash or what the heck a semi-colon is for.

What I do is write from the heart. I wonder if that is enough to make one a writer. What is more important? The heart or the mechanics. I have known more people who favor the mechanics than who favor the heart, and those who favor the mechanics tend to be stern perfectionists who can stifle any shred of creativity in people like me. They also tend to be more employed and more employable than me.

So, what makes somebody a writer? Am I a writer? Can I write anyway?