Dead Island Side Quests Walkthrough: Bloody Health Service
You get this quest in the lifeguard station. It's a pretty easy quest and you can complete it fast.
Dr. Jack says tells you he is stuck without medical supplies and that the infirmary door is locked, and asks you to break it.
Accept the quest and follow the prompt to break open the door.
Watch out, there are a few zombies inside the Infirmary! Dispose of them as soon as you have broken in.
Talk to Jack after killing the zombies to complete the quest.
Make sure to grab the painkillers from the desk, which you will need for another sidequest in the lighthouse.