We hope you won't encounter any medical problems during your stay in Innsbruck, but if you do, the following information might be useful for you.
There are many pharmacies in Innsbruck. They're usually open until 18h00, some close during lunch time.
Every night another pharmacy takes over the "emergency service". They're open all night long, but they're allowed to demand a surcharge on the normal price of their products (usually around 3 to 4 €). If you don't know which pharmacies are doing the emergency service, check the Internet or just go to the nearest pharmacy, they always display the names & addresses of today's emergency pharmacy at their front door.
There also is a smartphone app called Apo-App.
There is a list of all doctors ("niedergelassener Arzt") in Tyrol. You can look for the type of doctor (general practicioner, gynaecologist, etc.) as well as for the name or the adress of the doctor. You can even check if there's a doctor speaking your mother tongue ("erweiterte Suche" --> "Fremdsprachen").
A general practitioner is called "Allgemeinmediziner", "praktischer Arzt" or "Hausarzt".
Before going there, please check if your medical insurance will take over the costs or if you will have to pay them yourself.
Austria has a very good health care system and especially the main hospital in Innsbruck (Landeskrankenhaus Universitätsklinik Innsbruck) has an excellent reputation. It is a very big complex about 10 minutes by foot from the Golden Roof.
On the website of OeAD you find a lot of information on health insurance in Austria (who needs one, who can use the one from the home country, how to get an insurance, etc.).