Cough with breathlessness with normal HRCT and X ray may be related to airway disease like Asthma and small airway disease. A pulmonary function test should help in diagnosing airway disease. Since you have already shown a pulmonologist and if he feels there is no lung related issue, then doing CBC for anemia, ECG and 2 D ECHO for cardiac function should be the next step to evaluate. Symptoms of worsening breathlessness in lying down position or in the night during sleep suggest a cardiac cause. Also look for symptoms like palpitations and swelling in both legs, which will again suggest cardiac cause of breathlessness.