If you're self-conscious, you can't lead well.
To be confident, you have to own your story, your strengths and your weaknesses. You don't have to hide your weaknesses or fake confidence in an area where you are weak. You simply have to know yourself well. Like Baron said, when you are vulnerable, you're kind of invincible because there's nothing someone can tell you that you haven't said yourself.
So, to stop being self-conscious, to be a great leader - own your story.
Be confident in what your working with so you can serve people with your leadership.