Doctors warned people to stay away from the medical tent where patients were being treated in order to avoid contagion. This means to avoid the spread or transfer of diseases or infection. Contagion means the communication of illnesses from one person to another, most especially when in close contact.
I think that cringe means that a response to embarrasement. But right now in this text I think this word means that they didn't want that to happen. Or they thought that was not good. Hopefully it's right. I mean that's just my opinion. :D