Public Health and Psychiatry are probably linked in many ways. So you majoring in public health is not a mistake and you can learn a lot if you want to morph into psychiatry at a later time.
I personally would not mention to people that you are taking medication, i am on a small amount of anti-anxiety medication so i am not judging, but there is a stigma about medication.
I don't see why you should not be able to be a psychiatrist and you would not be a hypocrite for taking medication. I still would not mention it to anyone like EVER, because there is a stigma, they could think you
are unstable possibly or not up to the task or something. I would still go for it. This is gonna sound crazy but a lot of psychiatrists commit suicide hehe sorry to be a downer by mentioning it, but
it is weird how that happens, the people in charge of such a great position have so many underlying issues themselves. I think it is possibly because to be a psychiatrist you almost have to be a genius to
aquire all that knowledge, and genius and madness often go hand in hand. A lot of porn stars commit suicide too but that is another story, I am just saying, psychiatrists are not more screwed up than other professions necessarily