I have found that faith is something that every writer should have in his or her self. If you do not have faith in yourself as a writer then it will show in your work. The result is that you will not be able to keep your reader interested in what you are trying to say. I think that once you establish that you are the best writer you can be then you will be able to enjoy writing much better.
Forget all the contests. Forget the possibility of becoming published. When you write, it should be just you and the story brewing in your head. You should be able to get lost in what you have to say. You should be able to disregard that nagging voice in your head that tells you that you cannot do it. It is only out to destroy your faith in yourself.
Remind yourself every day that your faith in yourself is strong. That you can do anything you set your mind to as a writer or any other area of your life. If you do this you will go far in writing and in your life.