You say that you have all other coverages on your vehicles beside uninsured motorist property damage. This allows me to believe you have both comprehensive and collision coverage on your vehicle. If you do than you will be able to place a claim to your insurance company through the collision portion of your policy.

If you know the at-fault party, you can contact their insurance company directly.

Collision coverage covers damage to your car when your car hits, or is hit by, another vehicle, or other object. Pays to fix your vehicle less the deductible you choose.