Should I sue the negligent driver of car that caused an accident and resulted in an injury to me?

I'm assuming that the negligent driver you're talking about was the friend who gave you the ride, since the driver she tail-ended most certainly wasn't the one at fault here.

You probably need to sue your friend.  You sound like you have some serious problems here, that haven't fully resolved and perhaps haven't even been fully discovered yet (which isn't all that unusual in this sort of situation).  I would very strongly recommend that you take your case to a good personal injury lawyer.  It's possible the attorney will be able to get a fair settlement from your friend's insurance company without a lawsuit, but I wouldn't be too optimistic about that.

Your friends probably wouldn't even have to go to the trial.  From the way you describe the accident, and especially as a passenger, there's no way that you have any share of liability here, so the trial might only be to determine just how much you're entitled to in damages.