What has helped me overcome this is recognizing WHY we worry so much about what other people think in the first place. And I don't mean you or me specifically, but humans in general.
What you're describing, while maybe more intense than others, is 100% natural and actually makes sense given our evolution and our current situation as a species.
Over the course of human evolution, we spent that vast majority of time living in small tribes of roughly 30-50 people (exact numbers are debatable and don't really matter). Our brains literally evolved in an environment where we lived with, worked with, and took care of ONLY those people. Each individual person was completely dependent on the tribe, meaning if they were kicked out for any reason, they'd be dead within days or weeks. Because of this, our brains evolved to care A LOT about what our fellow tribe members thought about us, because for most of our history it was quite literally a matter of life and death.
Fast forward to the last few thousand years, where agriculture and other technologies caused our populations to skyrocket exponentially. Suddenly, we humans found ourselves living amongst many, many, many more people than our ancestors, yet we still have the same brains that they did (because evolution moves much slower than technology does).
So let me put it this way: today, between our families, coworkers, friends, and strangers that we pass by on the street, we interact with more humans every day than our ancestors ever saw IN THEIR ENTIRE LIFETIMES. And that's not even mentioning the millions of people at our fingertips on social media. And yet, our brains still think we're living in the tribal era, and that having people accept us is still a matter of life and death.
Logically we know it isn't life or death, but that doesn't matter. The parts of the brain that trigger the nervous system are the oldest parts of the brain, and they don't understand logic. All they understand is survival.
Reflecting on all of this has actually been extremely helpful for me. Because the mind likes to come up with ALL SORTS of stories surrounding any social anxiety I feel: "i'll never be accepted," "I'm good enough," "everyone hates me," "if I mess up, everyone will laugh at me," etc, etc. When in reality, the real and simple reason for my anxiety is that my brain thinks this is really important, even though it isn't.
So when that anxiety and the negative thoughts arise, simply acknowledge them. Notice how your body is responding to the situation, and reflect on how millions of years of evolution have instilled this amazing defense system in you. If you make a habit of this, rather than trying to resist the anxious thoughts or feelings, over time it will become easier not to get lost in them, and you will demonstrate to yourself that you will be okay no matter what others think of you.