other doctors do 15 minute med checks for such things as pain management, diabetes, cancer etc. it isn't unheard of, and it certainly isn't against the hippocratic oath. psychiatry is mostly about medication prescribing these days and it doesn't take that long to see how the medication is working out (e.g., assess side effects, look at the results of blood tests, write a script).

there are some psychiatrists who offer therapy... you might have more luck with checking out your local psychoanalytic training institute (if you have one). the cost of a 15 minute medication check up... well... you can expect to pay considerably more than that for a 50 minute psychotherapy session from a psychiatrist. many prefer not to see psychiatrists for therapy, anyway. maybe have a think about what qualities you would like in a therapist and might be that you can save yourself some money by seeing a counselor or a clinical psychologist or a social worker or something...