Your patient may be suffering from both problems at the same time- Cervical rib ( a part of thoracic outlet syndrome) and Cervical disc syndrome. So you have to address the both problems at the same time.

Asses range of motion ROM of Cervical spine, thoracic spine and shoulder joint. Assess areas of hypomobility and hypermobility in cervical and thoracic spine and any restiction in shoulder area. Assess the mobility of first ribs.

Assess tightness or spasm in muscles around cervical spine, thoracic spines, shoulder girdle, around glenohumeral joint and in upper limb.

Assess weakness in muscles around cervical spine, thoracic spine, around shoulder girdle, glenohumeral joint and upper limb.

Assess posture of patient especially cervical spine, thoracic spine and shoulder girdle.

Pain and inflammation in the thoracic spine can be relieved by use of modalities like heat, cold, diathermy, ultrasound, TENS, intermittent traction, etc

Mobilizations, manipulation can be used to increase range in the cervical spine, thoracic spine and shoulder girdle and joint and first ribs.

Tight muscles and fascia can be lenghtened or stretched by myofascial therapy of Stretch and spray, slow sustained stretching, Hold Relax and Contract relax PNF techniques. Muscles needing attention are scaleni, trapezius, pectoralis minor & major and other muscles around shoulder.

Muscles which are assessed as weak muscles should be gradually strengthened ny resisted and isometric exercises especially muscles shoulder girdle elevators and around the spine muscles & muscles of upper limb.

Poor postures should be corrected and good posture should be taught.

Any aggravation factor should be analysed and resolved.