It is not very difficult to find a pharmacy in Estonia, at least in the larger cities. It shouldn't be surprising that we also have functioning e-pharmacies, as well. The biggest pharmacy chains are Apotheka, Südameapteek, Benu Apteek, and Euroapteek. You can also check the Apteegiinfo site to find the pharmacy nearest to you, and compare product prices.
When you visit a pharmacy, you can use your ID card or passport to purchase your prescription. The pharmacist can easily find all necessary information from the online prescription centre, all by using your personal identification code. If medicine is being purchased for another person, then the person making the purchase must also know the recipient's personal identification code, as well.
Read more about digital prescriptions here: https://www.haigekassa.ee/en/people/pharmaceuticals/digital-prescription