Your own policy under the collision coverage will also either pay to fix or total the car less your deductible. Easier than going after the adverse driver. You technically can for the deductible paid but your carrier will likely do it for you if the other guy has insurance.
You probably can sue the other driver for pain and suffering if you want unless you chose a limitation on doing so to buy cheap coverage. If the other guy didn’t have insurance, you can get payment for that from your own company under uninsured motorists coverage. That about covers it.
Obviously, get checked out. You prolly at worst have soft tissue injuries that will just go away, but if you do need treatment, you want to confirm that as close to the accident as possible.