You don't have to be part of the LGBT community just because you are gay. You don't have to be or act a certain way and your sexuality doesn't need to define you or even play a huge role in your life.
Instead of focussing on what you perceive as a negative trait, maybe you and your T can look at the things in your life that you feel positively about. If you work on your self esteem more generally, perhaps you won't be so focussed on your sexuality, which is such a tiny part of who you are as a person.
My T says that 'the whole' is worth so much more than the sum of its parts. He is right - you are so much more than just your sexuality.