I have a herniated disc at t3-t4 from an accident burning pain in chest and muscle pain is this bad?

Back pain. The back pain can be caused by muscle strain, spinal stenosis, ruptured disc, nerve impingement ... It sounds like you are experiencing nerve pain. Before we can say if this bad, we need to know how severe is your conditions. Please see a pain management doctor or spine surgeon, you might benefit from a comprehensive evaluation and treatment.
Maybe. The burning pain in your chest is most likely due to the disc herniation touching/compressing the nerves that go to the area of your chest where you feel the pain. If the hernia gets bigger it can squeeze on that nerve further, and can cause permanent damage to this nerve, sometimes decompressing the nerve through surgery may help but not always, medications such as gabapentin, Cymbalta (duloxetine) may help.