Hi Aoura,
A big Aussie welcome to Susan's family. It's good of you to drop in and say "Hi". Hope you are able to find answers to your question, and you stay for a while.
There is a mountain of information, resources and friendship waiting for you here, you just need to jump in and start talking.
Firstly, let me put your mind at ease. You are NOT offending anyone here. Most of us in some way, shape or form have been through what you are going through. Don't stress yourself into thinking there is something wrong with you. There isn't.
I may suggest you reconnect with your therapist and discuss both the gender and depression issues. Does your therapist understand transgender issues? If not, find one that is. It will simplify the process. Secondly have a full blood test, particularly with respects to testerone and estrogen levels. An endocrinologist should be able to make sense of the findings.
By this time you should know whether you have GID (Gender Identity Disorder) or something else. Then and only then, you should start discussing your condition with your family. If you tell them any earlier, before you know, it will only serve to scare the hell out of them. Once you can tell them you have been medically diagnosed with whatever, they should be more accepting and supportive.
Keep in touch and let us know how you are coping, but in the meantime, be safe, well and happy.
Lotsa huggs
Catherine