No, you are not born a sinner. That's Catholic pagan teaching (the Catholics borrowed it from the pagans). You can't sin without the knowledge of it. You know right from wrong don't you? You and only YOU will be responsible for the choices you make.
Had Adam never sinned, the test would have been removed. There would be no sin or sinners. Once sin entered, YOU have to make the choice to understand what sin is, and how to not sin.