Must I try my case if I have been injured by someone else?

No, the short answer is no. Every case can, if the parties are willing, be settled. A settlement occurs when a defendant at last offers that amount of money which makes it more worthwhile for a plaintiff to resolve the case than to take the risk of trying the case. A good settlement sometimes has been said to make both parties unhappy, sometimes it actually does make both parties happy, but the bottom line on settlement is that it will not fully and fairly, provided adequate compensation to a client injured by negligence, unless the case is ready to be tried. Most cases are as a practical matter settled, not tried; but your case must be prepared for trial in almost every situation for the insurer to pay the full and fair settlement amount. And it must be well prepared!