I would encourage you to take a risk with your T and tell her.
Her reaction will tell you if she is a professional or... a bigot. If the latter, by all means an LGBT T might be the way to go for a deeper understanding of what you are going through.
I would invite you to give your T the opportunity to respond to you though. I know it is easier said than done but, as you said, you have lived a long time with this secret. And it is time for you to have a chance at happiness and to blossom. Unfortunately, you are the one who has to take the first step i.e. to tell people/T.
Again, this doesn't mean that you ought to suffer people's narrow-mindedness. You always have the option of finding a lesbian T if this one doesn't pan out. There is no shame in being gay..