It's Odense University Hospital, which is where the labels on the syringes Mikkel found said that the 'cure ' came from. That's why they came so far, looking for a cure. Even if it's not perfect, Mikkel and the base team back in Mora think it might be a jumping-off point for finding a real cure.
As to deep puncture wounds, in my own experience they take weeks to months to heal, and hurt for some while after that. Then, I wouldn't know about troll bites! But I heal quite fast, and have only experienced such hurts from the bites of a large dog, and from splintered wood, both of which would be clean in comparison. I wonder whether Sigrun has somehow managed to conceal an injury or infection from Mikkel? Can't quite see how, but it would fit with how she is acting.