The likely diagnosis in this patient is polymyositis, a type of inflammatory myopathy that causes muscle weakness and inflammation. The symptoms of proximal muscle weakness, difficulty swallowing, and nasal regurgitation are characteristic of polymyositis. The elevated creatine kinase level and abnormal EMG findings also support this diagnosis. The left hilar mass seen on chest x-ray may be unrelated or could suggest an underlying malignancy associated with the polymyositis. Further investigations, such as a muscle biopsy and imaging studies, may be necessary to confirm the diagnosis and identify any underlying causes.