Can i sue somebody who stop payment on a car loan that is in my name but they had the car. and it was repossessed?

Sure, but you'll have a hard time winning, in my opinion. First, is this agreement with your "friend" in writing? If not, it's your word against hers. Second, does she actually have any money to pay this judgment? I'm guessing that since she defaulted on the loan, she probably has little in the way of cash or assets to pay you. Third, do you even know where this "friend" is, and are you willing to pay the costs in money and time to chase the "friend" down and sue them? Bottom line - you took out a car loan in your name. Regardless of whatever deal you made with your "friend," you still owe this loan. It's your problem. Whether or not you can get anything back from the "friend," I don't know. My guess would be probably not.

If the friend agreed to pay, you can sue to enforce that agreement. You may be able to get a judgment (if you can prove the agreement) for the balance due, but not for any damage to your credit or the like. You were at all times responsible, as between you and the lender.

I agree. You have learned a valuable lesson. Do not ever do this again. You bought a car, gave it to someone who had no vested interest in it, and had no consequences it it did not get paid for.