I personally do not go to the doctors in San Juan Del Sur because I am a big fan of the international hospital in Managua, the Hospital Metropolitano Vivian Pellas, which is about 2 hours away from San Juan Del Sur.
If you have an emergency, you may go to Centro de Salud in San Juan Del Sur where they can stabilize you. Then, there is a hospital where they can do a surgery in Rivas (40 minutes away from San Juan Del Sur). They have custom private clinics where they can do surgeries and attend to emergencies. There are also several hospitals in Managua.