The car accident took place at February 28, 2020
Likely no. Our no-fault system makes your insurance company responsible for your medical bills. About the only way to get outside of the no-fault system and sue the other driver is if you suffered a serious impairment to a bodily function (e.g. paralysis, amputation, etc.). Back pain, usually, doesn't get you there.
As long as your car was insured and you suffered a serious impairment of a body function in the accident, you can sue the at-fault driver for pain and suffering damages.
