Can back/muscle issues cause shortness of breath? How about really bad posture?

Posture...not really. Bad posture should not cause shortness of breath. Even scoliosis does not have a significant impact on pulmonary function until a curve reaches around 50 degrees. If the back pain was related to a rib problem such as a fracture or costochondritis, then perhaps the pain itself could limit normal inspiration/expiration. Further evaluation and a physical exam by your physician would be helpful.