If you are registered as a resident in Portugal, then you are eligible for a Número Utente, which gives you access to all public health services and should be shown when visiting the health centre, for diagnostic tests and therapy, and also used at the pharmacy when purchasing prescription medications.
In Estremoz, getting your Número Utente it is a pretty straight-forward procedure. You simply go to the Centro de Saude from 9:00 to 13:00hrs and 14:00 to 17:30hrs, Monday to Friday, with the required documentation.