Am I on too many pain medicines? I am currently on norgesic, lyrica, (pregabalin) arcoxia, amitripyline, for my herniated disc.

See below. Sometimes, it takes more than one medication to treat a condition. The more important question is: are the medications helping or not helping. The second important question is : if the medications are causing side effects. Hopefully if they are helping you will not have to stay on them indefinitiely as most symptoms from a disc herniation calm down eventually.
It depends. If your symptoms are well controlled without side effects that are troublesome, you are probably ok. Some people would become quite sedated on that combination of meds. Arcoxia has not been approved for use in the usa due to concerns similar to the vioxx issues of high cardiovascular events such as heart attack and stroke. It continues to be marketed outside the usa.