First stop would be the Centro de Saude (health centre) with your EHIC to see if you can see a Dr but they may tell you to go to hospital Emergency. Second option is to go to one of the private clinics. You will have to pay for consultation but not too expensive, €75 or less usually. If you ask around there's no doubt a Chiropractor or Osteopath in VR.
As a result of a crushed vertebra 30+ years ago, I get back pain fairly regularly and I would suggest treating the pain with the usual and find an osteopath that knows what they're doing. In the meantime, keep stretching and moving.