I do not know what religion you are, but in my religous tradition - Judaism - a cohen simply can not be a doctor. Medicine, unfortunately involves touching the dead, and being in the same room with them. A cohen can not defile himself in the presence of cadavers. My understanding is that even rabbis who are cohens can not officiate at funerals or enter cemetaries.
For better or for worse (I think for better) the study of human cadavers for anatomy has been with medical study since, I believe, the University of Padua developed the pedagogical dissection of cadavers in the 1500's. The use of cadavers does not stop there. Cadavers are used in the study of surgical proceders and forensics. In a life-saving operation or procedure which does not work, may that not come to pass, the physician may in certain cases actually be touching a cadaver until the physician deems the continuance of the procedure to be futile. And so on and so forth.
I may be a medical student, but I have never been my own physician. I go to others regarding my own health care. I would never go to a doctor who had not dissected a cadaver: because the dissecting of a cadaver was in my personal case critical to what understanding of medicine that I have, and hope to acquire in the future.
But I am just one person. I do not know what religion you are. Maybe you could consult the authorities in your religion to see what they say. Someone on the forum suggested you investigate changing religions. Certainly you are free to do that. My religion imposes many constraints on my seemingly innate tendencies, expecially my proclivities to make mischief, or worse. In my case, I am prepared to give my life in the defense of my own religious beliefs. Unfortunately in one ugly anti-semitic encounter I had to be prepared to do just that. However, I survived the incident, obviously.
In America every person has, thanks be, freedom to choose.
