I'm not entirely certain this is best place to ask this question, so if there is a better place to ask this, please point me in the right direction. I'm interested in learning about the theories and practice of medicine in the ancient world, particularly in the mediterranean and near east in the Hellenistic period and classical antiquity, and things like humoral theory and responses to plagues. I'm not particularly interested in eastern medicine, though if there is a particularly interesting book on the topic you're excited to mention, please do! Looking at the books and resource list, I didn't see much on the topic of ancient medicine, and nothing regarding what I'm interested in.
Nutton, Vivian - Ancient Medicine might be a good place to begin. For near East, check out Ancient Egyptian Medicine by Nunn as a good starting point, and Hortsmanshoff's Magic and Rationality in Ancient Near Eastern and Graeco-Roman Medicine. For the import and rise in popularity of medicine in Greece, check out Wickkiser's Asklepios, Medicine and the Politics of Healing in Fifth-Century Greece. Jackson's Doctors and Diseases in the Roman Empire is also a good starting point.
Hope this helps!