Two general works may be of interest:
Oxford Handbook of Science and Medicine in the Classical World, edited by Paul Keyser and John Scarborough (released yesterday according to Google Books). In addition to Greco-Roman science and medicine, the first part has broad coverage of Mesopotamia, Egypt, India, and China.
The Cambridge Companion to Hippocrates, edited by Peter Pormann. The Cambridge site now gives October 2018 as the “expected online publication date.” There have been [forthcoming] references to chapters in this collection by, e.g., Chiara Thumiger and Brooke Holmes, though the contents do not seem to be up yet on the Cambridge site.