Wow. Artists have been doing self-portraits from the very first time they were able to view a calm water body. No, not like Narcissus, he went a little too far... No, what I mean is what we see. There are alot questions when we get into the idea of a "self". There are even people in the world who don't busy themselves with the idea of a "self".
Whether you believe in a "self" or not there are all kinds of ways to interpret the idea. You could look in a mirror, pin things you love to a board, put on make-up to express something hidden. At a very primitive level, self is our idea of identity. Think about all of the things that make up your identity: where you came from, your family, the things you like, the things you don't like, the things that you've made happen, the people who have gotten you there, the things that you didn't make happen. There are just so many things to get into with this idea, which is why it reappears in the arts over and over.
I'm not sure anyone really knows what that abstract idea of a "self" really is. Maybe it's supposed to be that way. Feel free to answer back with your own notions of self!