Can you fight your insurance company in a your fault accident after they fixed your car when it should have been totaled?

Absolutely! Regardless of fault, if you carry sufficient coverage (collision/comprehensive) you are entitled to have your vehicle either repaired to a "safe" standard, or a write-off payment received. The difficult part of proving such is in the time limits. DO NOT wait too long to seek a claim for a total loss. There is always the burden of proof in this case, where you may have damaged your vehicle "after" the fact, and after such repairs were made. Note any obvious damage, (eg. Doors not opening properly, engine problems) and have a certified body shop/mechanic inspect the vehicle RIGHT after the initial repairs are made. Generally an insurer will have an appraiser re-evaluate the damages to see if indeed, they were caused by the accident.