He is surrounded by girls by the sound of it, are there any boys around to make th pot more even, he sees gals dressing up and wants to belong . Does Dad play guy stuff with him, take him out for ball games ?
I agree completely with specialmom. Time to let that sitter go. What your son is going through could be a perfectly normal phase and pass if it's ignored. But if some dingbat who isn't even a family member is putting ideas in his head of what he should be and trying to define a sense of "normal" in his mind that is not something your family is comfortable with, then the sitter needs to go. Kids at this age are VERY impressionable and ready to believe and accept nearly anything anyone tells them about themselves--they're still very ego-centric. You don't want his sense of self to be mildly, moderately, or dramatically permanently influenced by some temporary person in his life that probably isn't even at full adult maturity herself (is she's under the age of 25).
I think we are all who we are. He very well could just be playing. My two boys went through a phase of dressing up as girls here and there as I had bought by accident at a thrift store a trunk of princess clothes and accessories. I took some pics that I'm sure I'll torture them with years from now. At 7, kids are often identifying with their own sex more than what you describe but that's okay. He'll either grow out of it or he won't. I wouldn't make a big deal out of it at all, ignore it.
I don't know though about your babysitter. Any sitter that 'wanted him to be a tranny' wouldn't work for me. I wouldn't want them to have ANY thoughts about what they wanted my kids to be for fear they put them in their head and in general, that is inappropriate for a sitter to be that involved. I'd ditch that sitter.
good luck