What happens if I don’t want to take the insurance company’s settlement offer? Do I have to file suit?

If the insurance company makes a reasonable settlement offer in response to your demand package, then the case settles and you are done.  However,  if you are not satisfied with the offer, then you can file a lawsuit and ultimately let a jury decide the value of your case.  It usually takes more than a year to finally get to trial -- sometimes several years.  However, the parties are free to settle at any time during the course of a lawsuit, and they usually do.