The teen years can be very rough on people. Often what kids think is abnormal is not. For example: It is not at all unusual for someone your age not to have a girlfriend. In fact, only about half of people have a significant romantic relationship before age 20. The other half find first love during the next 5 years. So keep doing what you are doing. Make friends. Refine your social skills and enjoy hanging out with the people you hang out with.
Secondly, lots of teens are afraid of rejection so they don’t do much inviting. They do respond, though, when someone else makes the first move. It seems that you have more courage than some of your friends. You do make the calls. My suggestion to you is that you relax and enjoy the fact that they respond.
It’s the so-called “weird kids” who often are the most successful in adult life. You are an individual. You don’t just follow the herd. You are doing normal things and feel just as normally abnormal as most teens do. I don’t see anything in your letter that raises alarms for me.
I wish you well.