As a citizen of Polish, can I go to a doctor in Slovakia and get a Slovak prescription to have a refund for the drug?

If you have an EHIC, you can go to a doctor and receive help on the same basis as Slovak citizens. If you need a prescription for medicines, you should see a doctor who has a contract with a health insurance company (Zdravotna Poistovna). Then it is possible to take advantage of the refund. The prescription for antibiotics is valid for 7 days, for chemotherapeutic agents – 3 days, and for medicines prescribed by the ambulance service – 1 day. Please remember that it is the doctor who provides the help who decides which service is necessary for you. It takes into account your state of health and the planned period of your stay in Slovakia. I enclose materials that may be of interest: https://www.gdziepolek.pl/artykuly/jak-kupic-leki-za-granica