One thing that stood out to me that you wrote was this:

It seems like, deep down, you enjoy solitude but would enjoy a friend or two to keep you company every now and then. I think in this case the most important thing is accepting that you're an introvert and like solitude and that there's nothing wrong with that. Secondly, realize that people that are of this nature don't always tend to be persons who are surrounded by tons of friends. It's not because there's something inherently wrong with them, but because most people are a bit more gregarious and tend to be surrounded by people that are more like them.

When I was younger I used to have a lot of the same feelings and hadn't really come to terms with who I was yet. It caused me a lot of grief knowing that I wasn't 'like' others. With time, though, I came to accept who I was, and I started seeking out people who were more like me. The end result was that I ended up finding friendships, and not only that, but friendships that were more meaningful.

At the end of the day you'll become more comfortable in your skin as time goes by, so don't sweat it. In the meantime try to break out of your shell and find people who have more in common with you, don't worry about being 'the life of the party' or doing things that make you uncomfortable.

Also, give 'Quiet' by Susan Cain a read, I think you might enjoy and find it enlightening.