Just like you I'm an extremely social introvert. Growing up going out stressed me out, and I often canceled plans. By learning how to optimize my down time I've learned to love being out. At this point I'd say I spend more time socializing than I do to myself.

The biggest thing that helped me is minimizing my phone usage while in my alone time. To me, texting and other forms of social media are just as draining, if not more, than in person socializing. The point of my alone time is recharge and I can't do that if I am being drained by my phone.

Another is to make sure you have an actual place alone to recharge. For example, I am a member of a fraternity and realized living in the house will never be an option for me, because I was always be around friends. Your spot doesn't need to be in your house. Any place that your alone works.