2600 B.C.: The Egyptian Order of Priest/ Physicians

Only certain priests were privileged to become physicians.  With only a few exceptions, "the office of these priests was hereditary and their privileges were exclusive; as the son trod with unvarying servility in the footsteps of his father."  (7, page 13)

As with society, the priest/physicians were divided by classes.  The higher classes of priests studied the first 36 Hermetic Books and became Chief Priests, the rest studied the last six Hermetic Books, thus becoming the Pastaphori, Military physicians, and the veterinary.

Here is a brief breakdown of the classes of priests who specialized in the healing arts. (3, page 16-17)(2, page 3-4)(7, page 13-14)

1. Chief Priests:  Also referred to as Sages, Soothsayers, Image Bearers, Magi, sorcerers, wise men or magicians.  These were the wisest of the priests/ physicians, and they were privileged to all the knowledge of the gods, and hence were responsible for reading the first 36 books of the Hermetic books. They were physicians of the "higher sciences."  These priests/physicians were responsible for "conjurations, dissolving the charms of the gods by prayer, interpretations of the revelations received by the sick during incubation in the temples."  (incubation will be described later) (3, page 16-17) They were more like the medicine men of the primitive world, "disolving the charms of the gods by prayer... magic and divination."  (2, page 4)  They were even mentioned by Moses "in the 7th and 8th chapters of Exodus, under the names of wise men, the sorcerers, and magicians, of Egypt, whom Pharaoh called in to rival the miracles performed by Moses." (7, page 13)
2. Pastaphori: The lower class of priests were responsible for studying the last six of the Hermetic books, and were responsible for visiting the sick and treating them.  They were your prototypical physicians, or ordinary physicians devoted specifically to medicine and the art of healing. Each of these physicians/ priests specialized in a certain ailment, such as internal medicine, dentistry, rectum, etc. They treated "anatomy, pathology, pharmacology, opthalmology, and gynecology." This profession probably morphed from the need of physicians to leave the temples, especially as medicine (particularly rational/civilized) evolved. 
3. Military physicians:  They essentially were Pastaphori who followed the military, and mainly were experts in treating battle wounds with salves, casts, splints, incantations, etc. Each of these also specialized.
4. Veterinary:  They specialized in health and healing of animals.  They specialized as well, as your cattle doctors, fowl doctors, etc. 

Physicians were free from the bondage of taxes, were paid by the collective, and profits belonged to the temple. The only obligation of the patient was to provide gifts, which sometimes included models of the organ fixed or operated on (such as an arm or leg), and these were kept at the temples as mementos, perhaps, of the healing powers of the gods. Likewise, "during war, or in the case of anyone falling ill upon a journey, the doctors were bound to render help gratis," (4, page 17) (9, page 25)(11, page 10)

So Egypt had a plethora of physicians who specialized in the various wounds and ailments that plagued Egyptian society.  Such specialization was both bad and good.  It was bad when you were sent a specialist who didn't specialize in what plagued you, such as if a physician who specialized in disorders of the rectum was sent to treat your son's dyspnea.

It was good when the physician treating you specialized in what ailed you.  For instance, if you were suffering from an asthma attack, you would benefit when your physician had access to opium or belladonna, both of which had the magical ability to ease your suffering.

 References:  See: "2600 B.C.: Egyptian Diagnosis and Treatment."