hi alana,
at the outset, sorry to know about your injury.
well, as far as there is no clinical signs of neurological injury, there should be no reason to worry at all.
i understand you are already on a brace which confirms immobilization of the segment. well, always log roll (move the body as a single segment) whenever you move in the bed to avoid pressure complications.
regarding standing, it is better to be on absolute rest at least for the first 2 weeks. the standing position is avoided because of the transfer, most often while moving to standing from sitting or lying there is a chance to bring in a torsional force to the spine which is contraindicated.
with respect to supplementation you may only if you have any other systemic illness. generally fracture healing of the vertebral body is good hence supplements are usually not necessary. rather drink plenty of fluids and take care of your dietary habits to avoid secondary problems like constipation etc.
well, movement is life and the principal segment of the human body is muscle so in order to avoid effects of immobility you may carry out mild to moderate spinal isometric exercises within the limits of your pain. please do not forget to add breathing exercises also to your exercise regimen.
last but not the least.. try to relate this particular phase positively. a positive mind has a very big role to play in healing.
take care & get well soon. feel free to contact in case you have any more queries.
cheers,
thomas