Many people do go into medicine because of personal experiences with disease. For example, a guy with a history of childhood cancer who becomes a pediatrician, or a girl with a thyroid tumor who discovers a love of endocrinology. Lots of people will write about their experiences in their applications and personal statements, and for the most part, that is looked on favorably.

Honestly, though, the one exception may be psychiatric history.
One of the things medical schools are thinking when they review applications is “can this person make it through to graduation?” Anything that makes them think the answer to that question could be “no” is a red flag.
A history of multiple psychiatric inpatient stays would probably be a red flag unless they were in the very distant past. The thought would be that someone with a history of, say, chronic depression, would have a much harder time handling the stress of medical school than a person without that history, and therefore would have a higher likelihood of dropping out. But it’s also sort of condition-dependent. Of course, admissions for something like substance abuse detox/rehab would probably preclude admission to medical school.

Many schools require incoming students to undergo a physical before starting school to certify that they don’t have any medical or psychiatric conditions that could hinder their studies. Some things may lead the school to put your acceptance on hold (like my school has done for students who were pregnant or had been recently diagnosed with cancer) until you are ready to start school, whereas other conditions may completely keep you out of medical school.
Unfortunately, the stigma that comes with psychiatric conditions is often strong even withinthe medical establishment. It is rare to find a physician outside the field of psychiatry who will admit to a personal or close family history of mental illness. (A fact which I personally find ridiculous.)

So basically what I’m telling you is that you want your admissions committee to have no qualms about accepting you, so be wise about what you write about in your application.