For emergency situations of any nature, dial 112!
In Estonia, pharmacies are called Apteek. The closest one to the university main building is in the bottom of the town hall as you enter the square. This pharmacy is also open 24 hours.
Information on health care and finding a practitioner can be found here.
Information on health insurance can be found here.
Estonian medical system presentation on 27 August
ESN Tartu presentation on 28 August
UT Academic Sports Club presentation on 28 August
UT museum presentation on 28 August