Yes, you'll certainly be called as a witness in the case. In fact, it is very likely that you will be deposed before trial.
In the event that a judgment were entered against you over and above the policy limits, it is possible that your assets could be exposed and seized to pay the judgment debt. However, as I said, the insurance attorney is going to try to settle the thing within policy limits. Also, if this girl has $18,000 in medical expenses, a judgment for even double or triple that would be a stretch - in my opinion. Thus, I really think you should be ok.
If the attorney can get the client's out-of-pocket expenses paid, a little for pain and suffering and a decent fee for a few phone calls and filing a complaint, that will likely make this go away. Your attorney is going to know how to handle this case, and chances are, he/she will know the plaintiff's attorney (will have had cases against him previously), so they'll know how to handle this.
Asking for 4 times the actual damages is not a request for punitive damages. Punitives are damages over and above compensatory damages (money to make the claimant whole again) to punish the defendant for some gross act of negligence
or wrongdoing. Thus, you should not have to worry about that either.
As I said, the best thing you can do is get the paperwork you're served to your insurance company asap in order to get an attorney working for you on this matter.