Let's be real. It happens to all of us. You're walking onto the third floor of the library, talking loudly about someone you just saw downstairs who is from your hometown, only to come across that same person coming out of the elevator at the exact same time. You stop mid-sentence and very obviously avoid this person, meanwhile sinking slowly but surely into the pits of public embarrassment. Yes, this example is extremely specific because it just happened to me about 10 minutes ago.
My point here is, it happens to all of us! Constantly! Whether we like it or not, we all embarrass ourselves sometimes. We are all going through the same, never-ending struggle of putting our pants on backward or tripping down the stairs. So, since we are all in this together, let's cut each other some slack! You get over public embarrassment by realizing that it happens to everyone. Take it in, feel the embarrassment for a minute or two, and let it out! You will get past it, and although it's a cliché, it's true that one day you will look back and laugh at yourself instead of cringe.
Accept the fact that you can't change your actions, as well. There is nothing that you can do to go back in time and un-rip your pants. So, once again, just accept it. Accept that you can't rewrite the past, and don't dwell on little things. All we can do is move forward, and let go of things that don't matter along the way. It is okay to mess up because no one is perfect! Even the Queen probably toots in public sometimes. And people probably laugh. But she's still the Queen.
The next time you just can't seem to get over your public embarrassment, try to let it go. You will breathe so much easier if you aren't consumed with parts of the past that you can't change.