I am curious if not having a BC drivers License or Health Card (I am covered by a Union in America for Health) will cause any red flags?
Do you have a drivers license at all? If you tell them you don't have one, that is not really a red flag, just uncommon but if you have a valid US license, they will take it as a sign that you are really living in the US as if you were living in BC, you should have exchanged it for a BC license within 90 days of moving.
They didn't really ask you to bring a health card but if they ask for it, I do think it would raise a red flag if you don't have one as most people who live in the province would.