Am I a lesbian trapped in a man's body?

You can identify as a lesbian if you wish but other lesbians won't be interested in you to date/relationship the main reason being that you have a male body.

Of course gay transgender people exist but sadly trans people often find they are mostly considered undateable. For example ,I identify as a ftm who likes females but no one wants a man with breasts and a vagina.

There are so many people with different thoughts on how they would like their body to be and what kind of people they would like to have a romantic relationship with that it is impossible to classify them all. If I had to put you in a recognized category I would have to say you are a straight male who likes to cross dress as a girl. You would probably be happiest with a straight girl who likes to cross dress as a boy.

Gender Therapists:

http://www.drbecky.com/therapists.html

Well, if you feel like a girl, you could be transgender. And that is definitely possible. Caitlyn Jenner is also MTF and was married to 3 women (but before she was Caitlyn).

Gay transgender people exist. You might be one of them, or you might just be a guy who likes wearing skirts and makeup. Nothing wrong with either of those things.

Gay transgenders do exist.

It seems as if the feeling of being a boy or a girl is pretty independent from who you want to go to bed with (boy or girl).

No. The body makes you the man

"Do gay transgender people even exist"

Gender identity and sexual orientation are completely separate things. Because they are transsexual people can be of any sexual orientation just like everyone else.

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if you feel female then you are female.of course you can be transgender and gay

I think you are confused.