So sorry to hear your story.
I have worked a lot in spinal units and while my background is in neurology and neuropsychology I now primarily practice in spine injuries and pain medicine rehabilitation. The following is just some general comments hopefully you will find helpful but not intending to replace your own doctors advice.
So the good news for you is that if you are walking and at home, albeit in pain, obviously the fractures must have been stable and not assoc with spinal cord damage or neurological loss. Fractures can remain very painful typically taking up to 3 months to heal and people often report very sudden relief about this time,even with vertebral crush fractures.
Controlling pain at this point is important for a number of reasons so something like oxycodone sounds appropriate and there is good evidence that adding a regular dose of simple acetominophen (paracetomol) has a synergistic effect enhancing analgesia.I dont use much by way of anti inflammatories after the first week or two and not a great fan of muscle relaxant's per se but the concurrent calming effect on the mind is sometimes useful. I tend to wean people off oxycodone as soon as practicable. Talk all this over with your doctor.
With uncomplicated fractures I advise people to keep mobile but not to overdo things,again I havent seen your CTs or examined you but assuming they are stable,uncomplicted (no neuro loss) etc. If this is the case, I spend time reassuring people that pain related to such light activity does not cause harm.This is important as otherwise a fear of activity can lead to avoidance and slower recoveries and other problems. Discuss how much activity is right for you with your doctor.
The biggest challenge many people have is with coping with the pain and its aftermath. Psychological influences like fear,uncertainty about the pain and when it will go, worry about your job, thinking about the trauma/incident over in your mind, anxiety and depression can affect your experience of pain and there is good neuroscience and evidence to support actively assessing and treating these sequelae leads to much better outcomes. I often refer my patients to specialised pain management psychologists to learn pain management strategies and to work through the various issues. Don't be shy in asking about this.It is important.
On a related note,try and avoid any medicolegal issues (if indeed relevant) if possible until you are recovered as they tend to mess with your mind unnecessarily.Try and get back to work on light duties as soon as possible. This is good for your recovery and hopefully your employer will be appreciative of your efforts.Try not to sweat it if they are not as it will only add to your suffering ( I know this is easier said than done but make the effort).
Finally when bones are healed we typically start people on graded exercise programs which boosts their confidence as well as conditions their bodies.
The vast majority of people have excellent and full recoveries so importantly try and remain positive. Remember this is a physical as well as mental challenge, recovering from trauma like this is harder than training elite athletes coz you have so much invested in it. Like athletes, however, it takes both physical and mental strategies.
My prescription for you is crank up MC with your favorite music and immerse yourself in a bit of music therapy to lift your spirits and distract from the pain a bit. Know that there are lots of us wishing a speedy recovery.
Once again,happy to give advice and encouragement but not replacing your own physician advice who is in the best position to treat you.PM me (not sure how that works here yet) anytime.