The answer is: Only if you let it. Please research "how to compartmentalize." Basically, you will learn to think about work only while at work, and not at any other time. You will also learn how not to be shocked at the sight of blood and guts, so you can focus on completing the medical treatment of the patients.
There are, of course, sometimes problems with compartmentalizing. Suppressing the trauma can cause it to flare up later, such as in PTSD. So, you will develop coping mechanisms. It could be physical exercise, it could be talking to a therapist - I find therapists to be very helpful, especially since they are non-judgemental.
One other aspect though, is the question of if you want to have a family. Sometimes first-responders begin to see only the evil in the world, and decide they do not want to have children. I would encourage you to try to focus on seeing the good in people - there is plenty of it out there, but you have to look for it.
If it turns out that this is not the right career for you, please do not give up on healthcare all together - there are many other opportunities out there. One example is X-ray technician.
Best of luck!