The character of the pain suggests a pleuritic type of pain. It occurs when there is irritation to pleural layers which cover the lungs. Pericarditis is one of the late and serious complications to be considered in post CABG patients presenting with pleuritic pain with pleuritic chest pain.
Pericarditis is inflammation of pericardium layers covering heart. Although pericarditis in itself is not often an emergency, this inflammation may sometimes produce massive effusion due to fluid accumulation in pericardium putting pressure on heart, resulting in a dangerous condition called cardiac tamponade. Patient may appear to be getting relief from symptoms like pain in such situation but suddenly worsens. In such a case urgent treatment to remove the fluid is necessary, sometimes requiring surgery.
Post CABG patients can also develop mild to moderate heart attacks. Although they often present as sudden worsening of crushing type of pain, Myocardial infarction should be considered in cases of chest pain.
The above two complications require immediate attention and I suggest you to take your father for a cardiologist consult, preferably through ER. Other causes like minor pleural effusions, improper healing of sternal wound or wound infection can irritate the pleura resulting in chest pain. Once the cause of the pain is determined treatment can be planned accordingly.
Hope this helps. Do get back with any further queries. Thank you.