You have failed to mention some very important information- What was the nature of the trauma? What sort of treatment was given?.
Because you have not mentioned about any surgical management, i lake it that you probably had a 'stable' burst fractures (with an intact posterior column) of the L4 & L5 vertebrae.A corset might have been prescribed.
Generally, in most spinal fractures,fracture stabilization occurs in about 6-12 weeks.Fracture stabilization refers to mainly healing of the ligaments and other soft tissues around the site of the fracture so that abnormal mobility becomes restricted.Full radiological bony union (as per plain X-Rays) may take an indefinite amount of time.
I can not possibly answer you precisely how long your fractures may take to heal(as it is highly variable).Regarding the medications, you must consult your orthopedic surgeon and he/she will be able to assist you regarding this.
MB BS, MS, FRCS(Edinburgh)