The following is based on my own knowledge - for your own case you should
consult an Orthodox Rabbi for a correct ruling. My wife, worked for the
Belinson Hospital blood bank and I served in the IDF as a paramedic. We had
to answer telephones with a change (left handed or picking up with one
finger). I had the right to give on my own up to six pills each of various
types to patients. I would cut up a ten individually wrapped package into
twos and ones for distribution and on Shabbot, I would not write the
patient's name -unless I had to call the doctor - a more serious
illness.(also done with a change)
Since you mentioned New York City, you have a good chance of working with
Jewish patients on Shabbot and you have a heter to save them. If you were
somewhere in the Yukon territory or the hills of the Philipines and the
chances of meeting a Jew to save him on Shabbot were close to zero, I
wouldn't advise such work.
As for residency in a hospital - my wife used to work when we first got
married on a second job in the blood bank.She would walk there from home. I
could even bring the kids to see her if I wished but she decided that being
a Mommy was more important to her. Are you willing to spend Seder Night or
Yom Kippur in residency? - This question you most ask yourself as patients
need medicines 365 days a year 24 hrs a day.
With prayers that Am Yisroel will be healthy,
Richard (Rachamim) Pauli