Hello.
Any fracture will take a minimum of 3-6weeks to heel when immobilised in the form of plaster, or brace.
Since the fracture happened at L1 , the lower back we can't immobilise it with a plaster, we ask patient to be in bed rest for 3 weeks and after 3 weeks, allow them to move around with a belt. But this line of management depends upon the type of fracture and involvement of the vertebral body. Some fractures are so severe that they require surgery to stabilise it.
Xray would have helped here.
Next Steps
If you had already visited an orthopaedician, then continue bed rest for the next one week or else please show it to some spine specialist.
if pain is not tolerable, please visit again.
Health Tips
Take full bed rest for next one week , avoid sitting and standing if you have to then please use a brace.
Also check for bone density if available to start anti osteoporotic medications that will help in fracture healing.