Self-conscious is when you feel extreme awareness of your appearance or actions. It is the knowledge of your own existence. Could feel uncomfortable at times. Self-consciousness is much more about what is external.
Self-awareness is when you can see yourself clearly with some objectivity with reflection and introspection. Self-awareness is much about what is going in internally.
If we can find a small wedge of detachment in your thinking, we can get a sense of either self-consciousness or self-awareness.
Developing a healthy sense of self requires that we know about both subjects, the value is the better you know yourself the better you know others which makes for healthier relationships.
Self-awareness is quite important because it allows us to deeply know ourselves better, what makes us tick, what makes us angry, happy, bored or interested. We can look honestly at our own actions with clarity and choose a wiser path.
Learning to have a healthy sense of self is a lifelong journey, there is no one way to learn, everyone is unique. It is so important to care enough about ourselves to take the time to know ourselves intimately.
You will gain confidence, insight, direction and goodness and no one can ever take that from you.