The adjuster for the other driver's insurance company keeps calling me. Do I have to give them my statement?

No. Often times an adjuster will attempt to pressure an injured person into giving a statement. In Texas, liability is not established on the basis of what information the other driver's insurance adjuster attempts to secure from you. You are not required to provide a statement to the other driver's insurance company's representative.  Remember, if you have serious injury, the adjuster's job is to try to save the insurance company's money - not protect your rights!  Rather than try to negotiate with a trained adjuster regarding your serious injuries, you should seek the advice of a board certified personal injury trial lawyer.