body injury in accident!!!

Had a car accident early this year in a shopping mall before one stop sign. I hit the back of a light truck which stopped at the stop sign and was going to turn left. I planned to turn right. I knew it was my fault. My car's left side was damaged, the light truck had almost nothing problem. The black driver told the police officer nobody was injured. But now his lawer sent me a letter the black guy had body injury. My liability for body injury covered by insurance was 15000. It is my first time. I need some advice. What if eventually the judgement says the compensation for body injury is more than $15000, should I pay by myself the extra part exceeding $15000?