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 healthcare system presentation
University of Tartu Museum presentation
UT Academic Sports Club presentation
International Student Ambassadors presentation
Erasmus Student Network Tartu presentation
Transportation system in Tartu presentation
Estonia as a Global Observatory presentation by David Ilmar Lepasaar Beecher