Yes. If there are any injuries or property damage, you need to call your insurer, even if you know you will not be making a claim. Even if it’s not your fault, it’s good to let your company know, and it may be helpful to you because they can help negotiate a settlement for you with the other driver’s insurer.
It’s best to let the professionals who are used to handling claims work on it on your behalf. Your company can also help cover your expenses if the other driver’s company is not moving quickly enough. Your company can negotiate with the other driver’s company to be paid back at a later time.