Welcome to the forum!
Do you know how many successful people have suffered from depression (both unipolar and bipolar)? In fact, it's a very interesting fact that many famous artists, politicians, etc. have been bipolar, and many people see this as part of the key to their ability. The shame is not in being depressed, but it can be in letting it get out of control and swallow you.
If you're bipolar, it's not really a question of whether or not you or anyone else likes the idea of being on meds: the simple fact is that without them, the illness gets out of control -- sooner or later. It sounds like you and, more so, your parents could do with learning more about the illness and getting past the "stigma" factor. Bp is not something you can simply choose to ignore and it'll go away (neither is unipolar depression for that matter). A good book I read on the subject was Miklowitz's Bipolar Disorder Survival Guide -- I recommend it highly, and you can get it through the Resources/Books section on the right of this page.
Please don't take any risks with your health at this point: your parents are your parents and, even if there's short-term alienation from them, in the long run at least you won't be alienating everyone because of how bp goes -- and your parents will only understand once they educate themselves on this condition a bit more, which is what must happen now -- once they understand, I'm sure they will support you, but that understanding is for them to foster and ultimately should not affect your decision on you wellbeing.
By the way, did you know that there's a bipolar board on this site too? Do pop by there any time you like -- we'd love to meet you (and it's a nice bunch of folks there too!).
People are not like fish: they do not work well battered.
When I'm not in my right mind, my left mind gets pretty crowded...
Co-Moderator, Bipolar Forum