The fear appeal is a common thing used in the media and basically boils down to trying to get someone do what you want them to do by providing them with an example that strikes fear if they wouldn't do that. A recent example would be Trump and his rhethoric about Mexicans and Muslims.
True with out sleep you would not be able to re gain energy you need to stay awake and alert
I'm not sure if there is a for sure answer for this, so I can only give my personal opinion.
The truth is if you care, you care. You can't really help that. There will be times where caring makes things unimaginably harder while other times, it makes you even stronger. The only real times where caring gets in the way is when you possibly lose a patient, or if you know you're going to. The only thing you can do is remind yourself that you are doing the best that you can/did the best that you can. If you know deep in your heart that you did everything you could possibly do, yes it will still hurt, but you will be able to forgive yourself and move on.
Perhaps there is no one dying, but caring about someone and seeing them hurt is difficult? Just take comfort in knowing that you are the one there to help heal them.
Hope this helps. :)
