Obviously you're not close to passing so that leaves you with no place to "go". Many public places now have "family" restrooms and while they aren't really intended for crossdressers, they are lockable and probably a better choice. I've never been to a place that had "Men" "Women" and "Other".
I don't think ther rest of us feel a "thrill" using the women's restroom, it's just more appropriate for those who come closer to passing.
You might have asked a security person if there was a private restroom you could use.
