Close the card. My ex managed to get ahold of one of my cards, my name only, and bought $900 worth of new tires. I didn't find out about it until it was too late and ended up stuck with that debt. As for the car, the loan being in both of your names is only to his advantage, if you're paying on time. But make sure to switch the title over to your name only, it's that's possible.
Starting Score: 528