Besides the obvious sketchiness... no, actually, I think the obvious sketchiness is really just the key part. Might be a bot - do you have your Facebook gender set to trans? I've had similar experiences on Skype with contact requests. The few times I've accepted, it immediately turned sexual.
I hate to say it, but it could also be harassment by someone you know. I don't know of a 'gender search' mechanism on Facebook.