My response:
I'll respond first with a comment concerning Racer's opinion about your credit, because that's the easiest part. Racer is absolutely correct in that regard - - and your credit will go into the dumper eventually when the bank sues you, as discussed below.
If you didn't already know, you need to understand some basic contract law. First, a contract requires "consideration" to be valid. What is consideration ? In the most common of contracts, and the most common form of consideration, the law is talking about "money" when we mean consideration - - that is, something of value passing from their hands to your hands; e.g., money to you so that you can buy the car. On the other side of the contract, the consideration passing back to the bank from you are your monthly payments plus "interest" - - another form of consideration, but money nonetheless. Without consideration, or when the consideration fails, there is no contract.
Now, on to your dilemma. You appear to argue that the car is now yours because the bank has, in effect, marked everything "paid in full". That is not, in and of itself, a true statement. The law also recognizes "unilateral mistake"; e.g., the bank's statement of "paid in full" was not "backed" by any form of "consideration (your money payments and interest).
Since money has not passed from your hands and into the hands of the bank, you have no proof that consideration was made by you in order to get that "paid in full" stamp on your papers. If you can't prove that you made payments, or paid in one lump sum for the car, the court will consider that the greater force of truth is that there was a "unilateral mistake" made by the bank, and that no "consideration" passed back to the bank from you. Therefore, a judge will render the "paid in full" a nullity, requiring you to return the car, and to pay attorney's fees and costs. This is because you knew, or should and could have known, that you never completed your end of the contract. If the bank wanted to get real nasty with you, they could also sue you for "Bad Faith", and perhaps, obtain punitive damages from you, also.
So, before this matter turns into a "mountain", rather than the mole hill that it currently is, I'd return the papers if I were you.
Good luck to you.
IAAL