Compensation is normally paid by the insurance company of the at-fault driver if you have to go to the doctor/hospital or if you have to miss work. You'll need to contact their insurer to begin the process unless you don't plan on getting medical attention for your injuries.
It is quite common for drivers to share fault in an accident. The amount your insurance is paying to the other driver is based on your percentage of fault in the accident.
Coverage & Claims
In the state of Rhode Island, medical coverage is not a legal requirement to meet the state insurance law so it is optional. "Full Coverage" refers to coverage for damage to your vehicle and doesn't necessarily include any other extras like rental car, roadside, or medical. Your best bet is to contact your insurance company and ask if your policy includes medical coverage for you and your passengers.