Yes, you can be sued in most states if you caused a car accident with injury. Even in no fault states, you can be sued in some accidents where the damages are beyond a certain level. Being served with lawsuit documents after a car accident is stressful, but keeping calm is important to make the best decisions.
It is common to be sued months or even years after a car accident. The first thing to do is to call your insurance company and tell them you are being sued. They should already be familiar with the accident. Next, call your attorney. Next, you will need to deny or accept what is alleged.
The case at this point could go to trial, with discovery being next. But after discovery is complete, both sides will try to reach a settlement. The worst case is the case will go to trial, and you could be responsible for any judgment beyond coverage limits, but this outcome is unlikely.