You might not be an introvert, but I’m sure you could gain from employing some of their coping strategies.
So, the way I would handle this problem is by creating a “happy place.” Somewhere where you can go to be free of rejection. I would fill this happy place with therapeutic things. Your favorite blankets, your favorite books, everything you like. Being here should recharge your batteries and get you ready to venture out again.
When I go to the bar, these days I bring my laptop. When I get there, I find a spot at the bar, order a beer, and set up my laptop. My laptop has everything I need in order for me to feel safe, comfortable, and happy, except for my music, which I keep on my phone, and I have earbuds in my laptop bag in case I need them.
It’s a safe place that I always have with me, that I can always retreat to when I start feeling discomfort.
The second thing you need is a way to recognize what you need in order to calm down. I don’t often need my earbuds and music at the bar, but I’ve learned to recognize when I do. If I feel really tired and cranky and crappy, music often cheers me up.
With all that in mind, go out and try to make friends. If you get rejected, retreat to your happy place until you feel ready to go back out again. As you go through this cycle over and over, you’ll start to do better and better. The amount of time needed in your safe place will drop, the amount of social rejection you can withstand before you have to retreat will go up. Eventually the amount of rejection you experience will drop too.