In my experience, both parents and doctors were much less likely to push the meds if I came up with some alternative plan.
I would tell them I don't like the meds and give some reasons - side-effects, mostly. Then I'd suggest something else, like 'Give me anti-depressants/anxiolytics and some talk therapy and if it doesn't help, we'll re-evaluate."
I had no intention of re-evaluating, but there were occasions where that approach kept me off drugs I didn't want.
It helps if you aren't talking about planes switching on your telly or whatever, though :-/