I fractured my back 3 montsh ago and right where the fracture is burns pretty badly. is this normal?

No: Burning can mean unhealed structures, inflammation or nerve pain. Many fractures of the spine also involve soft tissue injury, disc and nerve injury. After 3 months, it's time to follow-up with your doc to get more answers. Possible MRI for further diagnosis or other treatments should be considered. If I can help, then join my care team and virtual practice at www.healthtap.com/dr-clarkeholmes