If you have a NIE number and a social security than you should have a doctor assigned to you probably in your area, otherwise you can find here some doctors that speak english and can take care of you privately.
If you don't have a social security and are not registered with the local council don't waste a moment and head down to your closest town hall and get yourself registered. The process is called Empadronamiento and can be done in the central office in Raval if you can't find you local town hall. (C/ Rammellers on the square where the popular restaurant/cafe Kasparo is)