Since I am unsure how long ago you were in the motor vehicle accident, it will be difficult for me to determine proper types and doses of medications you should receive. However, one thing that I would like to mention is that the most important thing a physician can do for a sufferer of chronic pain is to help set realistic expectations. After serious injuries, it may be troubling, but it is not reasonable to expect that you will be pain-free in the long term, and the goal of therapy is often to provide enough pain relief that you can experience a satisfying quality of life.
That being said, your doses of Piroxicam and Lyrica are pretty standard for mild to moderate pain, but given the pain you are describing, a new pain regimen may be appropriate for you. Piroxicam is great for acute, inflammatory pain like that just after a car accident, or mild long-term pain. Lyrica is good for neuropathic pain, which is a type of nerve pain that people describe as "electrical" or "shooting".
My recommendation here, considering your history and how severe your pain sounds, I would speak with your doctor about a referral to a pain specialist. This is a special type of doctor that specializes in pain management, since it can be very complex and patient-specific. They typically cannot be seen unless referred by a primary doctor, and since pain control is often very difficult to manage even for a general doctor, a pain specialist may be the solution you are looking for.