My mother is bipolar, as is a coworker, and let me tell you how awful it can be for everyone around them when they go off their drugs. The coworker is in a supervisory position and it's just horrible.
SO, from MY standpoint... there aren't many things more frustrating than a rapid-cycling unmedicated bipolar nurse (or mother!).
As to your personal situation... I see absolutely no reason why you can't become a nurse. It's no one's business what chronic condition you have. Just stay on those meds!!