One thing I would add is that being a psychiatrist is not what a lot of people think it is. If you're picturing Freud-esque things like delivering therapy, CBT, psychoanalysis, etc and that is what you would really want to do as a career I would definitely recommend you look into becoming a clinical psychologist over a psychiatrist. Psychiatrists of course can also deliver such treatment but their main role is more usually to diagnose mental health problems, prescribe medication, and direct patients to clinical psychologists who will usually be the ones to deliver the therapy. Psychiatrists often oversee patients in a clinic but their training is medically based which is what allows them to prescribe medication. Personally while I considered going into clinical psychology for a while, I never wanted to be a psychiatrist after an old lecturer of mine went on a rant about how over-paid psychiatrists are when they often do not give much time to listen to the patients individual experience and often rush to prescribe medication without exploring therapy first.
Anyway, it really depends on what you are interested in- if medical school sounds good to you then why not go for it with psychiatry, but if your goal is to deliver psychological treatments then you will likely enjoy and excel far more going down the psychology route and specialising as a clinical psychologist.