Disclaimer: This is my own personal advice. It is different from what has been commented so far, but hope it might offer a different perspective or angle.
Don't believe your labels, even one's you give yourself. Why do you think you are introverted? Is it because you took some Carl Jungean-esque test like the Myers Briggs and it said you were? Is it because your parents and teachers always said you were "shy"? Is it because you have anxiety disorder or depression? You mentioned this last one might be it but aren't sure -- if you have a hunch, go talk to minimally a therapist to find out.
Toss all that shit out the window. You aren't your labels. You are exactly who you want to be.
If you don't want to be introverted anymore, don't be. As some one who was the "shy" kid and introverted from basically age 4 to 19, mainly staying inside and playing video games, it would probably shock most people to tell them that I consistently score "INTP" -- who cares. Take a pragmatic approach to it. If even the thought of being conversive, over communicating, and going to events exhausts you, that's not introversion that's probably some disorder -- you mentioned social anxiety, for me it was depression -- we are human and we were meant to communicate, be social, and relate to others. I am not saying that to say "so you are wrong" I am saying that so you understand. If there's something deep down there that is the root of that, address it. For me, going to therapy helped. For others -- the root of the social anxiety is a troubled pass: an abusive relationship, a missing father or mother, or a relationship that desperately needs mending. We put up our walls and think these things aren't affecting us, but they do. A lot of people think therapy is for people who have things "wrong" with them. I think therapy could help every single person on this earth, no shame in it at all.
The last advice -- treat it like a challenge. Have fun with it. Hack at it. Try different things. Read. A lot. Listen to your body. Best of luck on your quest!