Unfortunately, you cannot force the other insurance company to accept responsibility for the injuries so this is why you will need to seek a personal injury attorney to represent you. The attorney should be able to evaluate your case and give you an assessment of the likelihood of success if suit is necessary as well as the possible damages. Your attorney can obtain your medical records and make a demand on the other insurance company and it may then be willing to settle your case. If not, the attorney can file suit for you. The suit would be against the driver of the other vehicle and, if someone else owned it, possibly the owner as well. Good luck.
If your claim for injuries sustained as the direct result of the incident in which you were involved is being denied your only next option is to take the matter into litigation. Your best option for doing that is to speak with a personal injury attorney in your area and see what can be done. Generally, the initial consultation is free and without any obligation and most personal injury attorneys work on a contingency basis--that means that they will take on your case only if they see that it has some merit.
Disclaimer: I am a lawyer licensed in the State of Illinois only, and I am not your lawyer (unless you have been in my office and signed a contract). This communication is not intended as legal advice, and no attorney client relationship results. Please consult your own attorney for legal advice. This is for informational purposes only.
Of course your best course of action is to obtain a personal injury attorney to asses your legal options. Sometimes the threat of a lawsuit by an attorney can make the insurance company re-evaluate their position without actually having to file a lawsuit. However, if their position is still no to damages then look at the possibility of filing a lawsuit. Most personal injury attorneys work on a contingency fee in the State of Texas, so it should not cost you anything to hire an attorney.