Does liability cover my damages caused by a windstorm?

Unfortunately, no. The damage to your car will not be covered if you only have liability insurance. Liability insurance only covers damages and injuries that you cause to others. There is no coverage to repair any damages to your car. Comprehensive coverage would cover your car for damage caused by a storm. Typically you would also need to add collision coverage when adding comprehensive coverage. Collision coverage would cover your car if you cause an accident. Since you would be adding coverage to protect your car, the risk of having to pay out on a claim is higher. This means your rate will typically increase significantly. Check with your specific company if you are interested in adding the additional coverage for the exact rate. Keep in mind, adding the coverage now will not cover the damage that has already been done and you must disclose the damage when purchasing additional coverage. Good luck.