I don't think there is anything wrong with you. We all have our struggles to overcome. Some are easier than others, but it's possible to overcome them if you put in the effort.
I think it's wonderful that you're meeting people at the gym, so that is a great start! As far as hanging out with your friend, I have been there. What if you do something on your terms, meaning do something you would want to do possible on your own, but include her in the picture...? I wish I had better advice, but you are smart and will figure it out.
I don't have any awesome advice, but I do understand the struggle. I wish you the best and good luck!