Sorry but I don't have any experience with fractures of the back. I do know that typical fractures take 3-4 weeks to heal depending whether it is a compound fracture or not. However, I don't know about the back because there is constant pressure on it. Have you seen a doctor yet? I don't know that it can be surgically repaired unless they put it screws or something to hold it together.
As far as healing, calcium is the obvious help. My husband also takes glucosamine for joint health which may or may not help. I would think that if you get balanced nutrients that it would help. Eat a lot of vegetables and fruit to give your body the nutrients for healing (I know I don't want to give up pizza and hamburgers either! ) I am not a nutritionist by a long shot so I would ask your doctor or his nurse about that.
I hope that you heal quickly. Are you in a lot of pain from the fracture? How did you fracture it anyhow?