I agree, being an introvert isn't wrong, it's more about what energizes or drains you, socially speaking, and how you recharge. I know, because I am one, and It's something I've learned to work with. One thing I know my introversion makes me good at is tuning into details about people. So when someone messages me, I go check their profile or read a few of their posts. If I see common interests, I'll pick one of their experiences I share and ask a question. Occasionally I'll see a post I really appreciated, go check a profile, and if I see common interests or experiences, start a conversation myself. Those are two good options for starting to branch out of your reserve a bit. Good luck to you!
You don't need to improve yourself. Being an introvert isn't something bad. I think your question should be, "how do I improve my social self?" My advice would be to just do it. Just talk like you might to a family member or friend. You have to ease into the comfortable. That's how I do it at least.