Bank opened a credit card in my name without authorization?

I recently went into my bank to ask about lowering my interest rate, and they said there was nothing they could do. They did, however, say that I could open up a new credit card and do a balance transfer with 0% interest for 6 months. I declined the offer, but the woman helping me opened one up in my name anyway. I never signed anything, and never gave authorization. She also linked the new credit card to my bank account. Is this even legal? My husband and I just purchased a new home and are in the midst of escrow, and this could look bad. The bank says there is nothing they can do. They have already run my credit and the card is active, but with no charges. What can I do?