No, the level of hormones in your body has no affect on "who you need to be"
Like most males who have lived that life, I am small framed, and I have little muscle mass. I lack many things that most males have. But thats all meaningless, it just means that I am a male who is slightly different than other males
I dont need to now dress and act like a woman, cuz no matter what I do to my body, I am still a male
And there are also males who act more feminine in ways, and girls who act more masculine in ways. But they still would tell you they have no interest in being the other gender at all
It doesnt prove anything other than some people just dont act like others. I like cutesy stuff often, I like colorful things, I like bright colors and dont like black and grey, I enjoy being gentle over being hardened, I enjoy being creative, I feel more comfortable acting gentle and caring over acting stern and strong and junk, I generally appreciate a more softer sense of aesthetic over a more "practical" one, all these things apply to me entirely.
But Im still a male
So doing anything outside of that is only following a desire. If I choose to not acheive happiness by having some sense of "identity", and living in some way that I have come to obsess over, I can find a feeling of being content with what I have, and being happy with my peace of mind, over wanting what other people have that I dont. Its entirely possible, but you have to allow yourself to change your state of mind.