In the immediate aftermath of a world-wide nuclear war, any medical facilities that survive will be completely overwhelmed and there will be little capability to replace any supplies. Those that they have will soon be exhausted. Trauma and triage will be the order of the day. Medicine will almost immediately be thrown back a couple of hundred years. Any surviving surgeons will have to quickly learn how to perform amputations without benefit of anaesthesia.
Any surviving medical and nursing staff will have to act largely as supervision to newly recruited personnel. Sanitary procedures will be a challenge and the facilities will tend to have the odors and noises of centuries ago. It will be a quite different place than people associate with hospitals today. They will mainly be a place to take people to die.
There will also be many more psychiatric problems because portions of the surviving medicated population will become irrational and the ensuing events are likely to induce traumatic and pathological behavior in others.
Safety procedures should be even more rigidly enforced because the traumatic penalty for accidents will be ever more serious. Diagnostic procedures will be largely nil and surgical remedies that would have been commonplace will be undoable. Alternate older time remedies and procedures will have to be implemented where possible until pharmaceutical production can be reinstituted - which for most items will be months and years and for some possibly decades.
Medical Treatment of Radiation:
One of the major medical problems immediately facing the survivors will be that of dealing with survivors who have been subjected to radiation. Below are three documents that may be of benefit.
Pandamics may well be a major immediate part of the aftermath of Doomsday but I have put a VERY large body of information on that subject under the Recovery section. You can link to it here if you wish.