If I hit somebody's car and in the process of us resolving things her car was hit again by someone else, do I still have to pay damages?

Good question. Assuming you caused the damages to the other vehicle, you would only be responsible for the damges caused by you. If the car that you damaged was struck by a second vehicle, the driver of the second vehicle would be liable for the damages caused by him or her if that driver was careless and negligent.

Assuming you have insurance coverage for yourself and your vehicle, I would immediately place your claims representative on notice about the accident that you are writing about and the multiple impacts by two different vehicles.