If you have a car accident in someone else's car and weren't on the policy will that cover the damages to the car you hit?

It depends. Some insurance companies insure the driver and any car they drive whether it's a rental, or borrowed with permission from the registered owner.

Other insurance companies insure the car and only the drivers specified on the policy.

Check with your insurance. It's possible your insurance follows you, in which case the damage you caused to the car you were driving and the car you hit would be covered.