I was told that totalling a car likely takes place if the airbags deploy, or the damage approaches 75% of the cars value. If that's true, and your car is worth $15k, the damage would need to be in the $11000 range or beyond for an insurance company to total the car.
Your insurance company has an estimator who will determine the approximate cost to repair. If they total it, you'll receive an offer for the car (NEVER accept the first offer. They'll turn around and make you a better one). You may be able to buy the car back at some negotiated rate, and use the payout to repair it the way you see fit.
Sorry this happened. What type of tires were you running?