Just a warning for you all out there, you have ZERO medical in Poland, they will tell you to go private or just refuse to see you
What do you mean "refuse to see you"? You need to be on the rolls of a particular 'family doctor' and that's who you first go to when you're sick. You might call around a few different doctors to see if they will enroll you. Once you're enrolled you see them for free and they're supposed to give you referrals for more specialized care.
Otherwise you go private.
How well do you speak Polish? Most family doctors are not that eager to sign up people who will be difficult to communicate with.....
I'll add. I was at a conference last year where the European Health Card system was the subject of one of the papers. The result was that it's best to not have to ever use it.....