Insurance typically follows the vehicle first and driver second. That means that your insurance is primary and the co-worker's insurance is secondary or excess. Since you as the owner only have liability insurance it is not going to cover damage to the vehicle caused by running into a wall. You would need collision coverage for this.

You will need to contact and report the accident and damage to both of your insurance carriers. To see if your coworker's insurance will cover the damage their insurance company will probably assign a license claims adjuster to determine if his or her coverages will extend to your vehicle.