Use the adjective self-conscious to describe someone who is ill at ease or uncomfortable with himself. A self-conscious person might worry about how he looks or whether he's saying the right things.
Being self-conscious goes beyond just being aware of yourself — when you're self-conscious, you constantly question the way you appear to others. You might feel self-conscious when you stand in front of a group to give a speech, or when you're trying out for a movie or a play. The word first meant "conscious of one's own action" when it emerged in the 1680's, and by 1830's it had come to mean "preoccupied with one's own personality."