Brett is correct; in terms of medical documentation, there really isn't any way around it other than to come out. It'll be awkward, and some people might become too curious or inappropriate after they find out, but that's just the cost of doing business, unfortunately. My dermatologist, for example, was fascinated and made me pretty uncomfortable for an appointment or two, but now he's grown used to it and it never comes up anymore. Your doctors -- provided they aren't horrible -- will just make a note of it like they would with any other preexisting condition and move on.
I used to be terrified that my driver's license would out me constantly -- I look young, so I'm almost always carded at bars and clubs -- but I've been amazed at how many people either don't see my gender marker or just kind of gloss over it without processing what's actually written there. I've gotten my share of confused or searching looks, but 95% of the time, they continue to gender me correctly without even skipping a beat. I think people naturally put more stock in what they perceive with their own senses.
I will say I had some funny and surreal experiences over the phone when my voice first changed and I still had to officially identify myself with my birth name. They all assumed I was calling on behalf of a female relative or girlfriend and I had to patiently explain that actually, it was me. Thankfully, enough people have unique names these days that my explanation was usually taken at face value and not examined too closely.
