It'll take a visit to a doctor to determine this. The common symptoms of a fractured rib generally involve chest pain - not back pain. Here they are:
Mild to severe pain in the injured area.
Pain when you breathe.
Pain around the fracture when someone pushes on your breastbone.
If you can't breathe normally because of pain, you may:
Feel short of breath.
Feel anxious, restless, or scared.
Have a headache.
Feel dizzy, tired, or sleepy.
That said not everybody has the same symptoms - it takes a doctor with experience to tell what is associated with what. Burning pain is usually associated with damage to a nerve. I hope your physician can clear this up for you.
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