I don't have first-hand experience, but my ex would fit along the spectrum I think you are talking about. For a long time, she felt more comfortable dressing in women's clothes, then eventually gravitated more towards men's fashion. She had top-surgery, but I am not sure about her intentions for the full surgery. I personally don't think you have to necessarily be a part of the binary description of gender to consider yourself trans. It's all more of a spectrum...
I'm sorry you are having a difficult time with the psychiatrist and the general public. I'm glad though that you have a place to be open and yourself about it. I hope that continues. I also hope you get a response from someone who understands more fully.