So obviously social anxiety in the formal, medical sense is a real thing. I've had friends who have struggled with it, and had very good luck working with therapists. I'm sure that it's still a struggle for them, but at least from an external perspective, they seem to socialize and form relationships just as well as everyone else now.

Outside the formal anxiety sense, most people struggle with the negative feedback loop. The trick is that you can't simply turn it off - even if you're the best socializer in the history of humanity. For me, I set an informal timer (usually while journaling or in the shower) to intentionally introspect my interactions and pick one thing I felt I could have improved on ("I really wish I had said more than 'fine' when So-and-so asked me how my day was") and then move on.

One lesson that's hard, for me and I suspect others, is that while it's very important to be polite, it's not your job to make everyone else feel happy or complete - that's not an excuse to go around being a jerk, but also don't feel you owe anyone else something by default. It's enough to have a conversation about the weather or let the other person complain about their boss some and offer a bit of empathy.