Suing in car accident

[John213]

I was involved in a minor car accident, other driver is 100% liable. Other driver insurance already fix my car but rejected my personal injury claim. I have few questions. It's a small amount so I'm just thinking to do it in a small claims court.

Do I sue the driver or insurance company?

Does the other driver insurance responsible to protect/defend the other driver in the court?

If I win, does the driver pays or insurance pay?