I sympathize, because it took 4 or 5 phone calls adding up to more than 4 hours on the phone to get my insurance company to authorize a 140-day supply of a bunch of (very cheap) maintenance meds I take. In the end it worked out.
I have no experience with the Portuguese medical system, and I don't know whether mental-health drugs might be tricky, but this was my recent experience in Lyon when I woke up with a scary-red left eye to go along with the cough and slight sore throat I had had for more than a week:
It was (naturally) Sunday, so off I went to the pharmacy open that day. The pharmacist noted that I might need an antibiotic (not dispensed without a prescription), but sold me a box of ampules of eyewash, some non-antibiotic eyedrops, an expectorant for the cough, and some throat lozenges I asked for. The total cost was under 20€; it may have been less than 15€.
The eye was no better the next morning, so I made a same-day appointment with an English-speaking doctor recommended by the pharmacist. She spent at least 15 minutes with me, checking throat, ears and lungs as well as the eye. She also asked a few medical-history questions pertinent to my complaints (asthma? allergies? smoking?) She gave me several prescriptions. Her fee: 25€.
Back to the pharmacy I went, where I purchased the prescribed antibiotic eye ointment, oral antibiotics, probiotics and anti-nausea prescription meds (which I requested in case the antibiotic caused problems). Total cost: 34.58€ .
I suggest you try Googling to see whether you can find the cost of the drugs in Portugal. If it's low, that will relieve your mind to some degree. Then you can work on trying to find out ahead of time whether a GP will be able to prescribe the necessary medication.