Your health insurance will have 'recommended' centres to visit, give them a call so next time you'll know where to go.
Once, after getting knocked off my Vespa, I thought 'head to the Uni Hospital emergency room'. Doh. After nine hours of triage they eventually wanted to know what was wrong. The fact no-one even bothered to come over and see if my bleeding wounds were 'serious' or not, not to mention broken bones and blurred vision, made me vow not to go back.
I did though, another time, and it was equally slow. Wasn't any catastrophy in the city, just student doctors and nurses doing everything very slowly and with much discussion...
Next time I'm in the town centre, and need help, I'll go to my doctors clinic at Stadelhofenplatz. Immediate attention and no admin