How long after a car accident can you sue for damages from a uninsured motorist?

I was a penger in a high speed chase involving (the other driver, intoxicated) rear-ending us after we had to stop at a red light. I was pregnant at the time and I was on the phone with 911 the whole time we were getting chased, then we had to stop behind a couple vehicles at a red light, and next thing you know, he through his beer can out his truck widow then smashed into the back of us. The sheriff said he was fine to drive she didn't even give him a breathalyzer test. He had a suspended license and they just let his girlfriend drive him home. Now i have backpain and this horrible memory. I think this man should pay some how for his actions, even thought the law didn't take it into their own hands. Please help me find justice against this drunk driver, because next time it could be fatal.