What I would suggest is, first, stop driving the car before it gets worse, unless you have no other reasonable means of transportation. Second, consult an attorney. Third, based on the attorney's advise, get the car checked out by an independant dealership (expert opinion) to find out whether the problem can occure after only 500 miles.
If the contract says going to arbitration first, you must, or otherwise you are in a breach.
Most product liability torts require tangible damage or injury, which you don't have. I would suggest to find out from an attorney if you have any basis to sue under warranty or adhesion contract. Sounds like this seller knew the law and sold the junk car to you through a loophole. He might have known the car had problem but you have no proof. The problem surfaced before any injury takes place so that he could also have an assumption of risk defense to bar most of your product liability claims.