If your car insurance went up after an accident, you are not alone. Even one at-fault accident can raise your premium for years. The increase can feel especially frustrating if the accident was minor, the claim was small, or your driving record was otherwise clean. The good news is that a higher rate after an accident is not always permanent. You may not be able to erase the accident immediately, but you can often reduce the damage by shopping around, adjusting your coverage, asking about discounts, and avoiding another claim or ticket. Quick Answer: How to Reduce Car Insurance After More…