Wow. I feel for you, man.
It sounds like there are two major problems you face.
1. Low self-esteem and possible depression. In my experience those two demons go hand-in-hand. They are crippling for someone facing almost any kind of problem, not just relationship issues.
It's great that you're seeing a counselor or therapist. I hope it's someone you fit with, and who will give you powerful insights. A good therapist is wonderful; a poor one is a good reason to look for someone better.
I would guess it will be necessary for you to resolve the depression to some degree -- it's not simple -- and also work on your self-esteem even while you tackle the other issues. I'll write a bit more on both those things later if possible; I've struggled with both.
2. Your relationship and sexuality. Here's some good news: I read that you and your GF are honest and open with each other. That is terrific!
And I also feel self-awareness and integrity in your writing. Those things are of incredible value to you, and you already have them.
One thing that is really helpful would be to meet and, if possible, become friends with your GF's lover. That willingness on the part of a new lover to make friends seems to be one of the tests of polyamorous relationships: if a new partner is unwilling to meet the existing partner(s) then something may be going wrong. On the other hand, if she is willing to meet you and become friendly (maybe she already has?) then that makes everything stronger -- for instance, you and your GF will begin to share mutual-friend talk about her. "Oh, she did the silliest thing today...we laughed and laughed, and I wish you had been with us to see it..." That kind of sharing. Incredibly powerful relationship glue.
Anyway. I'd like to write more but I have to go earn a living. Take care!