I'm wondering how other people on here deal with embarrassing situations in front of a group?

Examples:

-To use a Seinfeld example, one time he was in a car at a stoplight scratching the side of his nose with one finger. Unfortunately for him, a carload full of acquaintances saw him through his windshield and it looked like he was picking his nose. Before he could respond, the light changed and the cars drove off.

-In my personal example, I'm a man suffering from an intersex condition that's impacted my appearance, and on rare occasion, it impacts voice so that my voice can be physiologically unpredictable when speaking loudly. In front of a room full of new coworkers and bosses, I addressed a customer by providing some helpful information, but my voice cracked and then sounded like a grouchy woman which shocked me. (That practically never happens.) And before I could excuse myself, the customer loudly criticized my tone and inaccurately called me, "mam," with lots of emphasis on, "mam." (And I've been trying to keep my coworkers from focusing on my gender.) The customer was aggressively glaring at me as if he were about to hit. So I walked off without explaining myself. I know people are going to gossip about this. And I have a letter of recommendation due out at the end of the month which might be impacted.

Don't situations like this just leave you feeling awful? What do YOU do?