The closest Hospital nearby is the Districtal Hospital in Evora 30km farway.. You can go for a clinic in Escoural 10km away. This is the palce that once a week a doctor comes to treat old people that due to lack of trasnportation of health problems can't afford to go to the nearest hospital or medical centre.
don't be scared. you'll find almost no one around. this is what happens all around the region of the Alentejo has it is the least populated region in Portugal.