I'm not sure what you were getting at with this correction, but at least in most states in the US, psychologists don't prescribe -- they're not MDs. I suppose probiotics are available over the counter so psychologists could recommend that a patient take them, but if it's "prescribing" in the sense of "writing a prescription," psychiatrists would be the ones to do it.
I was meaning shrink is derogatory for a mental health professional.
Shrink is not derogatory, it's colloquial. Eg "I'm going to see my shrink today". Like calling a general practitioner "doc", as opposed to quack.
I use it because I can never remember the difference between psychologists and psychiatrists.