You will need to report this accident to your insurance company and they will investigate your claim of what happened and the damage sustained to determine if it will covered by your collision or "other than collision", comprehensive, coverage. If it is determined that the damage is not covered by collision then it would probably be covered by your comprehensive coverage.

With either type of coverage you will have to pay the deductible as part of the claim process unless you have found the car or truck that is responsible for the piece of wood and they have taken responsibility for it flying at your vehicle. The deductible for your physical damage coverages does not change depending on if you were at fault for the incident that damaged your car or not. The deductible is chosen by the policyholder at the inception of the policy for any time you need to use these coverages.

Whether or not a surcharge will be issued will be determined by your insurance carrier normally. Typically since you were not at-fault for the incident a surcharge is not placed, but insurance companies rating systems can differ so find out from your agent how your specific provider's rates work. You may also be able to find out if your state has rules regarding insurance surcharges by contacting your state's Department of Insurance.