Sunflowere44....how wonderful it is that you are able to express your emotions this way!! And to look for answers! You should really feel proud of yourself
As you already know, there is a difference between being alone and being lonely. You said that you get hurt when people don't invite you places (I understand that!), but why wait to be invited? Invite someone to do something with you! Or simply go on your own and do things....you may meet potential friends by simply having fun on your own.
I am not a therapist but maybe you really would benefit from talking to a professional? I love that they are there when we really need to figure things out!!