spotlight effect
n. The tendency to believe that other people are paying closer attention to one's appearance and behavior than they really are.
Examples
2002
Oh, things sure took a bad turn. Mortifying, that's what it was. Such a big party — friends, co-workers — and you dumped that drink! How can you live with being such a klutz? Who there will ever forget it?

Take a deep breath. Stop obsessing. It probably wasn't as bad as you think. Not nearly. A growing body of research shows that far fewer people notice our gaffes than we believe as we pace the floor in private, going over and over the faux pas. And those who do notice judge us less harshly than we imagine. In a series of groundbreaking studies over the last two years, psychologists have shown that the "spotlight effect," as they call it, is a universal experience that distorts our egocentric notion about the degree to which people in groups, like parties and work gatherings, pay attention to us.
—Benedict Carey, “It's not all about you,” Los Angeles Times, January 13, 2002
1996 (earliest)
Having a bad hair day? Feel like too many people are watching you? Relax.

New studies say you get away with more than you think.

In a series of experiments, one of which subjected college students to the embarrassment of wearing a T-shirt with a picture of Barry Manilow, researchers conclude that people overestimate how much others pay attention to them. It's the spotlight effect, says psychologist Thomas Gilovich of Cornell University in New York. It's why you feel like a public failure if you stand in the corner or spill a drink at a party.

"You can relax," Gilovich said. "Many fewer people notice these and other embarrassing circumstances than you might think. … People tend to think the social spotlight shines more brightly on them than it does."
—Malcolm Ritter, “Researchers: People Don't Notice Your Shortcomings As Much As You Think,” Associated Press, August 12, 1996
Notes
Rule #2 — Nobody is thinking about you.

Yes, I know, you are certain that your friends are becoming your enemies; that your grocer, garbageman, clergyman, sister-in-law, and your dog are all of the opinion that you have put on weight, that you have lost your touch, that you have lost your mind; furthermore, you are convinced that everyone spends two-thirds of every day commenting on your disintegration, denigrating your work, plotting your assassination. I promise you: Nobody is thinking about you. They are thinking about themselves—just like you.
—Roger Rosenblatt, Rules for Aging, Harcourt, October 18, 2000