Seeing a counselor is a great way to start. I hope you are being as honest with her as you were in your letter.
Although I understand why you feel you need validation from someone else, the place to start is really with you. Currently, when you meet someone, you are kind of like a salesman who starts his pitch with “You wouldn’t want to buy this widget from someone like me, would you?” It doesn’t exactly invite someone to want to get close.
A meet-up may make you feel too vulnerable. I can suggest a couple of other things.
Talk to your therapist about finding a group therapy for you. Groups are run by therapists who help the members learn new skills for interacting with others. You will get feedback about how to be better at “personal sales” and you will get practice in using those skills with others in a safe place.
Volunteer! Find a project or charity or fundraiser in your community that attracts teen volunteers and get involved. When people are focused on getting something done, not on each other, relationships develop gradually and naturally. There isn’t the pressure to make friends.
I wish you well.