I'm suggesting splitting "Medical" into three smaller, more realistic specialties:
Trauma Care: Stabilizing people with serious wounds or injuries. This covers everything from First Aid to serious paramedic skills. This would be the skill used by combat medics, paramedics, and people with basic first aid.
Diagnostic / Therapeutic: The ability to diagnose and treat illnesses and other generally non-invasive procedures, from diagnosing and treating characters' illnesses to delivering a baby.
Surgery: The ability to perform invasive interventions to remove foreign objects and fix internal injuries and pathologies. This includes treating and repairing the damage from serious combat injuries.
For characters who graduate medical school, "Medical" becomes a three-way cascade skill. A level in any gives the character half a level of the other related skills; thus, a Surgeon 6 would be also be Trauma: 3 and Diagnostic / Therapeutic 3, and vice versa.
So for example - a character playing a general practitioner, a pediatrician, an internist, a diagnostician or some other medical specialty would take "Diagnostic/Therapeutic". Someone who specialized in any variety of surgery would, obviously, take "Surgery". A doctor specializing in Trauma or Emergency Medicine would take Trauma.
All would get the other two skills at half level.
For characters who are Registered Nurses: (i.e. who go through the "Nursing" careers in the military or civilian life), it's a two-way cascade between Trauma and Diagnostic/Therapeutic (Nurses as a rule don't do surgery). An "ER" nurse with "Medical (Trauma): 4" would also be "Medical: Diagnostic/Therapeutic: 2".
At the referee's further option, nurses who spend at least a term as "operating room nurses" and have a Medical (Trauma or Diagnostic/Therapeutic) of 6+ can be presumed to have Medical (Surgery) 0.
For characters who are military medics: Select "Trauma" (for combat corpsmen) and/or "Diagnostic/Therapeutic" (for a hospital orderly). Selecting either will give a level "0" skill in the other skill, plus a level "0" in Surgery.