This is a deep meta question; not the response you give others. When you ask yourself, “how do I feel,” is that answer you synthesize, the answer you draw from the edge of your conscious and unconscious self; is this answer a reference to the immediately preceding past of your inner experience, or is the answer from some self aware inner entity that exists in the ever changing experience of right now?
Reading How Emotions Are Made by Lisa Feldman Barret and A Liberated Mind by Steven Hayes will answer your question. More broadly, emotion construction theory and relational frame theory will answer your question.
Self awareness is just a set of relational frames. It is a building, a palace if you will, made out of blocks of thoughts and relational frames. Feelings are that too. You can use self-awareness to examine feelings (e.g. “I am sad that I failed”). However, you can also create emotions based on your sense of self (“I failed, and therefore I am sad”).