Legal Question in Personal Injury in Florida

Yes. You should contact the company's vehicle insurance company and make a claim under their property damage coverage. It will be an "adversarial" relationship, as opposed to a contract relationship as you would have under your own collision coverage; but in cases of such clear liability as yours, most will voluntarily settle your damage claim with you for either the cost of reasonable repairs or the fair market value of your vehicle, whichever is less.