Ok, speaking as a working Paramedic I can tell you from our side of things that most of our care is without regard to the gender or apparent gender of the patient. Honesty is your best policy.
Having said that, EMS is still very much manland. There is also an overabundance of GLBTs working in the field now, and with most of the oldtimers retireing, you're about as likely to get someone completely indifferent.
The medical information we need is limited to your past medical history, medications and allergies. Oh and we do need your legal name, that's a billing issue. Me, personally, I would refer to you in the gender you're presenting in as well I as discreetly as possible explain your situation to the ER and if your name was Steve but you preferred Alice, I would try to make that known as well.
Most of the EMTs and Medics I work with tend to follow the same belief, but then again I work in a big city.