No, actually, such thing has not been proven. Gender is nothing more than the stereotypes and roles that society expect from each sex. And your brain is still part of your body and every cell of your brain (like the rest of your cells) is either male of female. Even IF you were capable of proving that some men have a "feminine" brain, that doesn't mean they are women. There are some men that are shorter than many women, but that doesn't mean these men are women either.

Sex is about reproduction. We're an anisogamic species, which means we reproduce through the production of specialized cells with half the DNA (gametes) of different size. Male individuals are the ones who produce small gametes (spermatozoon) and females are the ones who produce large gametes (ovum). Then, a spermatozoon and a ovum fuse to form the zygoto, restoring this way the normal amount of DNA. Some species are hermaphrodites, which means they can produce both male and female gametes. Humans are not hermaphrodites, though. There are several genes involved in sex determination in humans, but the golden star is the SRY gen. Basically, if this gen is present the embryo will develope as male, if not it will develop as female. As this gen is located in the Y chromosome, XX individuals are females and XY individuals are males. There are some people who have a disorder of sexual development (DSD), but they are rare and they are still either male or female, i.e. they don't produce a third type of gamete.