There are several private and public hospitals in Yangon, but the fees, service and quality may vary. There are also some useful pharmacies in town.
AA Pharmacy Just north of Sule Paya.
International SOS Clinic Your best bet in Yangon for emergencies, this clinic claims to be able to work with just about any international health insurance and has a 24-hour emergency centre with an expat doctor.
Pun Hlaing International Clinic This is your best bet for centrally located healthcare.