Generally speaking you would only be compensated for the injuries you sustained and the pain and suffering you endured. Insurance companies do not compensate people for a "what if." In your case, the extent of the damages could have been much more severe had the toxic waste become airborne and caused you additional injuries. Because it did not, the content likely will not be considered. In my opinion, better to have a case with a lower value and not be dealing with the possible injestion of toxic materials.
You should consult a local personal injury attorney who can answer your questions more specifically.
The only thing I can think of that may make the hazzardous waste relevant is if you had some mental reaction of fear that it was leaked and may have effected you. This would be an element of your emotional distress claim on top of the normal pain and suffering.
But dont make things up, if the above did not happen to do not claim it, everybody will see through a false claim
The fact that he was carrying hzardous waste is not an issue unless the hazardous waste contributed tot he accident The fact taht he was at fault is important becasue it means he is responsible for any damages resulting fromt he accident. the act that your injuries are soft tissue afects the potential settlement as juries usually give lower awards for soft tissue injuries as opposed to injuries involving broken bones or injuries that require surgery. The fact that he works for a trucking company is important. The company is responsible for its driver's actions. The company will have adequate insurance to cover wahterver damages you might have siustained. Also, jurors to to give larger awards against companies than they give against individuals. It is easier to have sympathy for an individual defednant than a company.
The most important factor is how severe is your injury. If you are back to normal after physical therapy, the settlement value is not worht much. If you have a permanent injury, the case may have some value.