You're working in a setting where loose fitting gender neutral scrubs
are the norm. After starting your transition, other than the name change, physical changes will not be immediately visible to your co-workers.
I'd suggest working with your therapist to develop a timetable both at work, and in your personal life, regarding using your new name, makeup, jewelry, etc
In terms of discrimination, you'd be legally protected if you were in Chicago, but I don't know what the law is in NM. Much of the opposition will come from ignorance. Is there an advocacy group you can contact that can assist you in providing education on both a unit, and on an institutional level?
Good luck in your journey