It sounds very much like you have a left extension pattern (sometimes also described as a Left AIC/ Right BC pattern). This is a common pattern in humans due to natural and normal asymmetries in human anatomy and neurology, but can become problematic when the pattern becomes heavily engrained.
In this pattern, the left hemipelvis becomes forwardly and externally rotated, the left half of the spine becomes extended relative the right, the entire spine rotates to the right, and the thorax counter-rotates back to the left above the T8 vertebrae. Needless to say, this affects everything from scapular mechanics to breathing mechanics and spacial awareness.
Treatment is multifaceted and begins with breathing retraining and repositioning of the pelvis and rib cage. Standard upper back exercises are very (very) unlikely to help. Seek out a Postural Restoration Institute (PRI) Certified physical therapist for an assessment and treatment.