Can a minor’s parents be sued for pain and suffering if the minor got into an accident?

Always the people liable for the injuries screaming "scam" as if that makes it so. You have insurance and they will address the claims handling and determine if the case is a "scam" or not. That stated, YES, if your son was driving your vehicle and crashed into someone, you are responsible for the damages done as if you were driving the car, under the dangerous instrumentality doctrine. That you don't like that or don't want to pay or the insurance rate hikes from the loss issues, is of no consideration. There a many instances where a person that appears uninjured at the scene develops pain when the adrenaline wears off or has injuries show up later. Its so common its actually addressed  in most hospital discharge papers.