Studies have shown that mental illness and substance abuse are present at much higher rates in the medical field than many others. See
http://www.thelancet.com/journals/lancet/article/PIIS0140-6736(11)60145-1/fulltext for a decent overview. Anecdotally, I have known several medical professionals who have struggled with these issues. When I was on my psychiatry rotation, a medical student at my school was admitted onto our floor for suicidal ideation. One of my classmates was using cocaine regularly. One girl almost certainly had an eating disorder. Several were alcoholics. A lot of people abused stimulants. Several had to take personal leaves of absences. Other than Ambien, antidepressants were probably the most commonly prescribed medication by our student health; I would guess that maybe a quarter of my classmates were on them or receiving therapy at some point during their medical school. And I went to a school with an incredibly supportive administration with a tremendous amount of access to mental health needs.
Many people who struggle with mental illness manage to survive medical school, residency, fellowship, etc. The reality is that the medical field is very stressful and still suffers from the archaic attitude view that the suffering is part of the training (especially prominent in the surgical specialties).
However, not all schools are the same. There are schools that treat their students and residents relatively well. Seek out those places if you're afraid the stress is going to lead you to self harm. The quoted 16 hour a day 6 day a week for IM residents is not the reality in many programs. I'm a resident currently, and I almost never work those hours for days on end, and my program is probably more malignant than most. There are actually a few that take the work hours very seriously and actively try to give their residents a good quality of life. Nevertheless, there are other severe stressors in just taking care of sick people, filling out endless reams of paperwork, having too little time during the day to do your work, not having enough personal time to relax or exercise, managing your personal life, etc. Those are not trivial, and they alone are enough to push some people over the edge. You should think very carefully about what kind of life you want, and remember that every year of your life is around 1% of your life. Make sure the sacrifices are worth it.
Also, never reveal your problem with cutting to the admission committee. Do they reveal to you that four students dropped out last year because they were unhappy? No. Everyone plays up their strengths and pretends they have no weaknesses. It's just how it works.