Without a medical card you need to pay for visits, also your GP decides where he forwards you to, if he forwards you to a private specialist that’s where you need to go, and if you don’t have a medical card you will have to pay for that as well.

In THEORY the public system is free, but:

• Your GP NEEDS to forward you. Despite having a family history of heart conditions mine refused to forward me to a cardiologist.
• Some specialists simply aren’t available on the public system, my wife needed a psychiatrist and the waiting time was 1.5 YEARS
• You still need to pay for your visit, sure that’s a low value and it caps at €800 per year, but that’s still NOT free