I can sympathise with this. Couple it with the fact that in the UK we’re not recognised at all and have no legal protection, and the whole issue gets a heap more hairy.
Some support groups aren’t for everyone — heck, some aren’t even well-run. It may be worth seeking out another in your area, or finding an online support group. Don’t give up on pursuing whatever you need to make you happy and comfortable, whatever form your social transition takes. (I would only advise against hormones without a doctor overseeing — I’ve known people do it, but it’s generally unadvisable.)
I can point you to a few nonbinary communities on Facebook, if you have an account there, where you’ll be welcomed and accepted for exactly who and what you are. Just shoot me a private note, or DM me on twitter (@lexberju — I’ve set it so anyone can DM me) if you’d like to know more. And don’t give up. You’re far from alone.