I’m no shrink, but I was a cop for thirty years. An unwashed mental had a very distinct, very strong, very unpleasant body odor compared to an unwashed sane person. They both stank, but the mental was totally different. Something was definitely out of kilter with his body chemistry.
I don’t know about the body emitting different odors, as you have experienced. But there is definitely a difference in body chemistry. My brain does not produce the correct amount of serotonin.
And, if I am on an antidepressant alone, my body does not process it so that it only alleviates my depression. An antidepressant will kick my system into complete mania, an uncomfortable, nervous, highly talkative, edgy, state. In those who suffer depression by itself, it only aids their depression. My brain does not process the antidepressant as others do.
Also, my sister and I have been on some of the same anti-convulsant medications. For her, it stops her epileptic seizures. For me, it is just another medication that I use to help with the bipolar disorder.
So, understanding chemistry in any illness is important. Without understanding body chemistry, and in my case brain chemistry, doctors would never be able to prescribe any medications. So, I tend to believe in going back to basics and finding the source of the problem.