If you want to keep your car then normally you would request this of the insurance company and if they allow you to do so then the salvage value of the vehicle is taken out of the settlement (for the car's actual cash value) you would receive for the vehicle. When you take a settlement for the car's ACV then you usually cannot sue the driver for additional monies. 

According to the Texas Department of Insurance (TDI) consumer for auto insurance, an insurance company will pay for repairs or replacement only up to the car's actual cash value. Actual cash value is the amount that your car would have sold for before the accident

The car insurance consumer guide speaks about the issue you are having by noting that sometimes the insurance company may want to total your car, but you would prefer to have it repaired instead. You normally can keep your car if you are willing to subtract its salvage value from the insurance settlement. First make sure the cost to repair the car will not exceed the car's actual cash value. To find out the salvage value, contact local salvage yards for estimates

If your insurance company totals your car but you cannot reach an agreement on the amount to be paid, you can demand an appraisal. Appraisal allows you and the company to hire separate damage appraisers. The two appraisers choose a third appraiser to act as an umpire. The appraisers then review your claim, and the umpire rules on any disagreements. The appraisal decision is binding, but only as to the amount of the loss.

For more information on what your consumer rights are in Texas regarding the totaling of a vehicle and auto insurance claims in general, contact the TDI at their site or at 1-800-252-3439.