I transitioned in place and my family, friends, coworkers, clients, etc. all know about my past and the circumstances of my birth. It is significantly more difficult to teach people to use the right pronouns and name with you after 25 years of doing things one way. So I completely understand why you would want a fresh start where no one knows.
Honestly? I'd say you're fine. If the place you live now is relatively close to where you're from, I'd be cautious. Especially if where you are now is more of a destination that people travel to (a bigger city, place with cool landmarks, etc.), since you'd hypothetically be more likely to encounter people visiting from your old town. If your friends are on Facebook, maybe take a look through their friends list and see if you recognize any names of people who may know you.
But if it was a big move, I think you're fine. I'm of the belief that the only people who need to know are intimate partners and medical personnel who are directly involved in my treatment. So if your girlfriend doesn't know, I would find a way to tell her. It's infinitely more complicated to do after you've started dating someone though.