It's funny how I could totally relate to this post; making friends was also hard for me. Mostly people came to me because of what they wanted.
But at some point I started praying and asking God to send genuine friends to me. By the end of my undergraduate and NYSC year, I made a few good friends that have stuck around even after 9 years.
Though I am still learning how to socialize, last year I was intentional about it, and I started with my local church. Instead of going home after service, I just stayed around to greet a few persons and also volunteered in some church programs like outreach.
I think you need to be patient with yourself while making some intentional steps.