You should file a claim with your insurance and (also) with the semi's insurance. Your insurance will handle the car damages asap and odds are will be settled w/in a week. Now the semi's may take awhile, since they need to verify that the semi driver is at fault, before they pay you a dime. So, if you don't go with your insurance, then the semi's might take weeks/months before they agree to pay you.
Car damages are black/white. Insurance pays the amount to fix your car. If totaled, then they pay the ACV of the value. There is NO negotiation and get paid for the damages or the value.
Since injured, is another reason to file with your insurance, since odds are, you might have medical payment coverage or PIP, which pays for all of your medical bills. If neither, then will need your health insurance to pay the medical bills. The semi or at fault company does NOT pay for your medical bills, since there is no contract like your auto insurance or health insurance.
Now, depending on your injury, then the semi company (after) you have completed all of your medical treatment, will then ask for copies of your medical bills, and then get all of your medical reports from all doctors that treated you. Then after they review these, you would most likely be eligible for an injury settlement which is (reimbursement) of the medical bills, any loss wages, then (adds) pain and suffering.
A lawyer, your choice. All lawyers wont do (nothing) about your car damages, since there is no money in that. The only thing that will interest a lawyer is injuries, since when you settle, then they take 33% or more of (your) settlement. But, after the lawyers take 33%, then what (you) the client gets, could be (less) than the lawyers.
retired auto adjuster