If one side of the arm feels sore frequently, consider cervical spondylosis or frozen shoulder.
Cervical spondylosis can manifest as a sore feeling in the arm, either unilaterally or bilaterally, when the nerve roots are compressed.
Frozen shoulder usually manifests as discomfort in one side of the arm, with the soreness being more pronounced in the acute phase.
In addition to this, soreness on one side of the arm may be due to over-activity in that side of the arm and a build-up of lactic acid that irritates the muscle tissue, or it may be caused by a fracture, sprain, joint dislocation and nerve damage in that side of the arm.