Yes. You can be sued for the injuries and damages caused by your own negligence. The insurance on the company truck will most likely pay the claim. They will also provide an attorney to represent you in the event you are sued personally. Make sure the accident is reported to the company's insurance carrier. And, if you are ever served with a lawsuit be sure to give the documents immediately to the insurance company so they can defend you.
Best advice is find out what happened to the car. Contact the impound lot. They will tell you if the police have put a hold on the car. If there is a hold on the car, I would suggest you hire an attorney before talking to the police.
Most insurance companies will permit you to use of a rental car until the repairs are made or your car is declared a total loss. Contact immediately the at-fault driver's insurance company and talk to them about providing a replacement vehicle to you.
Report the claim immediately to your insurance carrier. Let them handle the injury claim. Your own insurance company will hire a lawyer to represent you, if a civil lawsuit is filed against you. Although, you may want to consider hiring your own attorney to represent you at traffic court.
Keep track of your doctor visits, mileage, lost wages and all expenses related to the injuries you suffered in the car crash. Your journal is discoverable so anything else you write in your journal might one day be used by the other side.
Police officers can write tickets based on the evidence they gathered while investigating the accident including statements made by the drivers and purported witnesses. Suggest you hire an attorney to represent you at traffic court and fight the ticket.
Report the accident to your own insurance company. They might cover the claim under uninsured motorist coverage, if you have it. And, give serious consideration to hiring a local personal injury attorney who is willing to on a contingency fee basis.