I've had my fair share of public embarrassment, most of which is because of my drunk blackout stories. How I deal with it:
Just remember that no one will remember the fool you made out of yourself in some months or so. People have lives and they aren't sitting the whole day thinking about what you did. You remember it because you felt somehow humiliated, and that's normal. But know that everybody is embarrassed about something, so just shake it off or even laugh at yourself. By doing that, you'll accept that you are human and there is nothing wrong in being awkward or whatever.