You can become a doctor. This is because you will be able to protect your patients in the process of healing them. This is because it will be difficult to do the two tasks at the same time in different departments.
I feel you should be a doctor. More money more benefits, but HUGE responsibility. A police officer is much more dangerous, but its easier to become one. Both requires tremendous effort and commitment though.
You really need to know more about what each of them do, how much people enjoy or dislike their jobs, and what career paths there are before you decide. They are both so different. I have worked in both fields and there are pros and cons for both.