You can access the free healthcare system in Romania is you are an EU citizen holding an EHIC card. However, the standards are generally poor and corruption is rife so it’s not recommended.
Bucharest hospitals are reasonably well equipped but in smaller towns, there may be a shortage of vital supplies. You can usually obtain Medication but don’t expect the brands that you know as Romania favours generic drug.
It’s not advisable to rely on the state health system. The standards don’t hold up to scrutiny and anyone arriving from a country which has reasonably good healthcare will find Romania severely lacking.
The good news is that the private sector is much better; so taking out your own cover will provide you with access to a vastly improved service and supplies. Clinics cover more trivial illnesses and injuries while private hospitals deal with serious conditions.
If you regularly purchase over the counter medication, it could be worth checking the availability within Romania. Many medications which you purchase easily in your home country may require a prescription in Romania.