Can i jogg or run with a compression fracture to t6 with slight kyphosis at that level? what about sports?

Not really: I would rather do swimming , it may help as traction. But first you must treat the causes of compression fracture and kyphoscolisis. There are special therapies, may be a team of orthopedist and physical therapy will be able to help you.

Depends: This depends if it is painful or not & if it is new or healed. Weight bearing exercise stimulates bone to be denser. If it does not bother you to run even if an acute fracture, it should be ok to run. If not acute, sports are ok as long as you are being treated for decreased bone density if present. If this was an acute fracture & is thought to be unstable, you need your physician to guide you.

Yes: Is the fx heal?Do you have any pain?If the answer is no you can engage in sports and jog and run.Fx of t6 are very stable fx specially if the compression is minimal and do not extend to the pedicules.At your age should not be any problem with those activities.

Light exercise: You may engage in light exercise once the fracture is heeled without pain. You should investigate the reason for the compression fracture and see if you have risks of future fractures such as osteoporosis or osteopenia. This may be tested with a bone mineral density test.