I was hurt in a car accident. Will the other driver's insurance pay for my medical treatment and time off work?

Even if the other driver's insurance company assumes liability, or admits the other driver was at fault, they won't pay for your medical treatment, diagnostic tests, therapy, surgeries and lost income as these bills come due.  A settlement or verdict in an injury case is usually one lump sum amount of money and must fairly compensate you for everything you have lost - medical expenses, permanent injury, disfigurement, pain, lost income, future medical care and future lost income.  
A settlement is a contract resolving your automobile accident injury claim for an agreed amount and is voluntary - no one can force you to settle your car accident case (or any other type of case).  Of course, the insurance company is not required to settle your injury claim either.