That is sweet to share such an emotional issue. I think that how we respond to and deal with death is very personal which makes us unique. I think it is important to embrace your pain.
When I was in nursing school and giving my first IM injection, I nearly fainted. I went into the bathroom and put my head between my legs and cried. Then I cried because I was afraid I would not be able to make it through school. A very wise nursing instructor (who I never had) shared some thoughts with me. She said it might help to focus on the good things I was doing for this patient. I had to process that over time and it has helped me through some bad times.