I think it's a lot harder to make friends as an adult than it is as a child as we are very self critical. How you see yourself is often not how others see you and it is worth keeping an open mind about other school mum's as they likely have the same worries even if they don't voice them. I don't have a secret stash of friends near you so I can't help with that but I wonder if it's worth asking yourself a couple of things to work out your options; what do you want from a friendship; one on one time, family time with them, days out, just a quick coffee, a shared interest etc? I'd also then have a think about what you like to do with your own time as an introvert; reading a book, going for a walk, art, etc and then find an opportunity to do that where others do the same; book club, clubs at your local library etc. You could start small just doing the activity alongside others while you build the courage to talk or even walking to pick your kids up and just setting yourself a challenge of smiling at 5 other people then build from there. A lot of the emphasis is with you working out what you want, what you feel comfortable with, being open-minded and pushing yourself. You have overcome your first challenge which is sharing this with hundreds of people! Best of luck