I am an introvert. I have been for my whole life. Sometimes, I just need to get away from people and recharge. Other times, I just run out of things to say. It can be very awkward, sitting there, when you're the only one not engaging with a group of friends. My brain just doesn't work under pressure like that. I'm the guy that says, "Oh! I should have said..." an hour after the conversation is over.

I do genuinely like people, however. I like to interact and have conversations with them and be generally social. This has always seemed contradictory, to me. I stuck the label of "introvert" on myself a long time ago, and there hasn't been much looking back since. The label felt good. It felt right. It was comfortable.
Several years ago, when my dad died, I had an incidental conversation with my sister. We had (obviously) had a couple of rough days and finally got a moment to decompress. She told me that she was impressed with how helpful and supportive I had been for everybody, and how much I had matured over the years. I casually said something like, "Yeah, I'm a real rock."
For some reason, that thought stuck in my head and I kept coming back to it in the following days. I hadn't realized it at the time, but I had been a rock. I had taken on responsibilities that no one would have expected me to. I had acted selflessly through the grief and exhaustion I was feeling to ensure that I was there for the people who needed me. I was strong, and it was so natural for me that I din't even realize that I was.
This epiphany just blew me away. I was strong. I had emotional fortitude. I was so much closer to my ideal self than I had realized. It was this deep sense of confidence that finally enabled me to push my introverted limits a little bit.
I started socializing more. Perhaps, the sense of confidence that I had acquired made me a better conversationalist. But more importantly, I wasn't nearly as self-conscious as I had been in the past. I had let go of the outcome of the interactions. I just didn't care as much what that person thought of me walking away from the conversation. I was much more comfortable with who I was. I still consider my self an introvert. However, I am no longer afraid to be extroverted. I still get nervous going into new situations, but my underlying confidence enables me to at least show up and experience them.
If you are struggling with introversion or low self esteem, you don't have to let it limit you. Try to visualize who your ideal self is, and find your quite confidence by trying to be that person. In time, you will have the epiphany that YOU are the prize.