Is it possible to be allergic to vitamins ie biotin/vitamin b supplement? how long before a vitamin is out of your system? 1 day?

Yes, about a day: One can not be allergic to a pure vitamin but can certainly be allergic to a vitamin supplement as they can contain corn, yeast, gluten (all common allergens) and various fillers and binders. More pure supplements from companies like Pure Encapsulations and Thorne tend to be better tolerated. And B vitamins (except B12) should leave your body within a day or so.