I have no emotions or thoughts while caring for the dying people sometimes makes my skin crawl...
Why do you feel that way?
To be honest sometimes it feels good almost refreshing.
I can understand why wanting to feel emotionless when dealing with people that could potentially pass away. I feel it's important to show emotions and sympathy for the people when they're in that position, you should try to show some empathy towards them to make them feel better. Continuing to feel emotionless about that situation could affect you mentally down the line.
Maybe I don't feel anything because I don't care anymore.
I think if your emotionlessness is cutting into the quality of care you can provide others it might be good to talk with someone. Dealing with death and suffering all day can be really hard on people, have you considered finding a different job?