Quick summary: I was rear-ended at a stop light about 1 1/2

Quick summary: I was rear-ended at a stop light about 1 1/2 months ago. I started a claim with my insurance company and they took care of paying me for my car (it was a total loss since she hit me hard enough to bend the frame~30+mph). I did not go to the doctor because I was not in a major amount of pain. I had some stiffness in my neck and the place where my seat broke below my shoulder blades and the base was sore. I treated it with advil and gave it some time. Since my policy only covers $25/day, the only car we had in town for that price was a cobalt. However, it hurt my back to get in/out (I told her adjuster this when I spoke to her). The only other car they had to sit off the ground was a Kia Sportage which (as I found out later) cost an extra $16/day. When I finally got my payment 20 days later for my replacement, I had to pay the extra amount myself (appx $400). Her company refused to pay more than the $25 per day my insurance covered. They sent me a check for $300 which said for full and final payment (that's what the personal injury adjuster said I was owed for time and medicine). I cashed the check because I needed to pay my at least some of the credit card bill on which the rental was paid. I did go to the doctor last Monday (MLK day) for them to check my back (I had to use my personal health insurance + co-pay). They took an X-ray, prescribed some muscle relaxwers and additional anti-inflammatory because she sai I had some muscle spasms in my back at the two places perviously mentioned. Bottom line, I just want to be indemnified for my expenses. Her insurance company is saying they will not pay anything else on this claim. So, is it possible to sue the insurance company or should I sue the insured for these damages? Any helpful suggestions would be greatly welcomed!