> physiological and outside the expertise of a psychiatrist

did you mean to say psychologist? In the US at least, psychiatry is a medical practice area. Writing Rx scrips requires pharmacological training, so you need to hold an MD amd pass medical boards etc. Not sure if DO route is even an option.

Psychology otoh can be practixed with a Psy.D (clinical focus) or Ph.D (research focus) no MD, residency involved.