It is the hardest spot to be in, looking at yourself laying there.
Even the Great Master George Lucas knew that. (lol) (Empire Strikes Back...swamps of Dagobah)
If it's really still bothering you this far out, you need to talk to a professional. I have had several instances like that, where I could completely see myself in the position of the patient or the family members, whose lives are permanently altered because of a random event. You will not forget this guy, or the looks on everyone's faces, but the sharpness of it all will fade with time.
I don't think at all that this means this career is not for you. That was a shocking first day, and even if all you had was routine calls, they would have stuck with you for a long time. Find someone to talk this out with...then re-evaluate.
People like you, who feel empathy, can go on to make the best medics. Heartless people moving slabs of meat, not so much.