What exactly is a Biomechanical Analysis, and how viable are they when dealing with an auto accident case?

I was rear-ended a year ago sitting still at a traffic light in Dallas, TX. There was minimum damage to my vehicle, as well as the vehicle that struck me. However, I sustained neck & back injuries, primarily my neck. So, I filed a claim with GEICO and received a payment for $931.33 for the damages to my vehicle. Initially, my medical claim was denied, but was later reopened. I received therapy for about 6 months, which I paid for out of pocket, and upon completion I submitted all of my bills and the requested documentation. My medical expenses totaled $2090 and loss of wages were $1677. The most I've been offered to settle is $1591.20, after I rejected the first two offers of $1291.20 and $1441. The adjuster, as well as her supervisor, both agree with a "Biomechanical Analysis" that was ran for my accident which reports I didn't need treatment and that my body would've healed itself within 21 days. My claim is currently closed, but can be reopened if I'm willing to accept their offer.