Pain85,
Most thoracic vertebral body compression fractures, due to a traumatic event (not due to osteoporosis), will consolidate, and be held pretty much out to length by the rib cage. Those, most patients do not have too much problem with pain in the region, no any nerve problems.
However, it seems that you are in the small percentage that does have problems.
Unfortunately, you seem not be able to manage this with pharmaceuticals.
As to whether or not a chiropractor could realign your spine, without causing any nerve damage? That would be unlikely. You do not have a normal vertebral architecture. It sounds like the disc complexes are involved. Trying to manually shift a damaged vertebra, with damaged disc complexes, would probably be asking for the nerves to be compressed by the damaged disc material.
For that vertebra to be realigned, it would probably take a spinal surgery, to fuse the T3, T4, T5 vertebrae. However, this is something that you should discuss with your spine surgeon. He/she is the best person to obtain information from.
Sorry that you are allergic to all of the medications that could help you.
Has your pain management physician considered a spinal stimulator for your pain? That would be another option for you to discuss with your physician.
Sorry about your problems.
As to the safety of a spinal manipulation, you might want to contact your spine surgeon, who has access to your imaging studies, and knows your case.
Good luck.
Hope you find something to take care of your discomfort.