In previous episode Sam gets hit in the side of the head with a gun and shows bruising and bleeding when he returns to the office that night. The beginning of this episode , which is the following morning, Sam doesn't have any marks on the side of his head.
The disease is initially diagnosed as typhoid fever (diarrhea, dehydration, fever, throwing up, significant stomach/intestines pain)the stomach problems are a large part of the disease. But later at the hospital Sam refers to the outbreak of typhus, which is a completely different disease caused by another vector, and more closely matches the symptoms discussed. Both diseases have a fever and sometimes a rash, however typhus is rarer and has more disastrous effects.
Sam and Naomi send pictures of the nun's rash to Dell so that he can find and consult an infectious disease doctor to help with the diagnosis. In later seasons, it is revealed that before switching specialties to alternative medicine, Pete's specialty was infectious disease.