Medical science was never the most developed of Creation's lores... it was never important in a world where nigh-immortal god-kings, immune from scarring and disease, determined what avenues of knowledge would be pursued. Even during the heights of the First Age, there was little need to make medicine a significant priority, manpower was plentiful and the technologies of that time allowed replacements to be trained readily should useful cogs falter. Yet, even if it was the first budget item to be cut, by their nature the Celestial Exalted transform what they touch, the Solar Exalted elevate it, and so there were numerous medical developments: some of these focused on infrastructure to prevent problems before they could occur (such as clean water systems) but the vast majority were cures to drive out illnesses or infections that took hold. Development of drugs for other purposes, intoxicants and analgesics, also occurred on a significant scale, seeing perhaps the greatest heights of all medical efforts in the First Age... not surprising, as the Exalted had use for such potions as well.
Much of this knowledge was lost to Creation following the Usurpation... the production of cures to stop mass outbreaks (and the purification of water and food supplies) was a function of extensive systems of infrastructure which the Dragonblooded Shogunate struggled to maintain, and which were finally shattered beyond repair by the events of the Great Contagion. With these great losses came diminishment... some methods and medicines were lost entirely, some retained in a lesser form... Acupuncture, developed by the Celestial Exalts to carefully map the flows and interactions of their bodies to find greater efficiency in Charm and attunement, serves as an example, its practitioners having basic understanding of chakra and flow based on charts carefully handed down across generations, with little grasp of the true underlying principles.
It is in the field of surgery that the Realm of the Dragonblooded can claim some small ascendance. By their nature, the Dragonblooded find their interactions with mortals more personal, their powers applied to individuals and not so great that they are beyond equal by the unExalted. When the Scarlet Empress ascended to power, the population not only of Creation's Terrestrials but of its mortals had been reduced to a shadow of its former self, every member of the population was needed to mortar brick or sow field. Thus, she created a system of public health through Her Benevolent Stewards of Health and Utility, based on more personal preventative measures (as example, instead of commoners drinking water passed through a purification system, they had to be taught to identify and avoid tainted water sources) alongside early intervention to stop medical issues before they became worse. Whereas in the First Age of the Solar Exalted medicine was the art of curing the sick so that illness or infirmity was not the end of a life, in the Empress' Age of Sorrows it is the art of making sure they do not become sick... for once they are, they cannot be saved.
The Realm gets little credit for its successes in medicine... of course its enemies both Threshold and divine denigrate its accomplishments, but its own ruling Dragonblooded rarely understand the accomplishments of their own regime. Of great aid to mortals but basically irrelevant to the divine Exalted, such things as boiling water before drinking, or even the masterful surgical techniques innovated by Ragara Bhagwei to excise infections before they claim a limb, often escape the notice of even those who might take credit for them.
However, were one to term medicine in the Realm 'advanced' could give the wrong impression. In a world where the local butcher or barber is also the village surgeon, if a village has any such practitioner at all, the standard to which the Realm is compared is not difficult to exceed. It is not a happy day to suffer an ailment in Creation, within the Realm's borders or not.
Medicine is practiced using Medicine (Ability), though preparation of medications may also involve Craft Water (Ability) and the Thaumaturgy path of Alchemy... a cook can brew mundane potions without Medicine, so long as they work with proper instructions, while thaumaturgical preparations are beyond even the most knowledgeable medical practitioners. Accurate performance of Acupuncture can be accomplished by the Medicine ability, though some innovation and deeper understandings may require contribution from Occult (Ability).