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 english speaking doctors who 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. With this, you can then go to the Social Security office and they will register you, and assign you the nearest doctor.