I agree that it's silly to say that you should reveal that you're Bipolar at the outset. I wouldn't want to do that for fear of discrimination; I would want my physical symptoms to be taken seriously and would be afraid they would not, or not entirely, if I revealed MI.
That said, when in the ED, they are automatically and definitely going to ask you what meds you are on. From there, they will want to know why (I know, I'm a health care worker). But they would ask you that even if you were not on MI meds, they want to know why you're on every med you're taking in order to get an accurate history. Which is all to say that, in just giving them a list of your meds, they will find out you have BD anyway.
I hope the vertigo has resolved. I know people who have suffered from that, and it sounds horrific!