There are no particular health risks in Greece, but during the hot summer it can be easy to develop dehydration and sun stroke /burn relatively quickly. Using minor precautions such as sunscreens, drinking water or wearing light clothing, sunglasses and hats can prevent most of it. Try to avoid staying in the direct sun during the hours when the sun is at its highest position (11 am-3 pm during summer months).
Santorini has all the expected emergency care of a tourist intense location. The main Santorini health center is located in Fira and five additional health and first aid stations can be found in Emporio, Kamari, Oia, Pirgos, and Thirassia. There are pharmacies everywhere that can provide medications and other first aid items that you may not have brought with you. Various specialized doctors can also be found throughout the island.