It was good that your doctor considered whooping cough (Pertussis) as a possibility because there has been a great increase whooping cough in adults, in recent years and Azithromycin is the treatment of choice. You may have to take more than one 4 day course of the drug to get maximum benefit. Also your description of a cough lasting several minutes is most typical of this disease.
It is worrisome that you are short of breath and it suggests that, despite the initially clear Chest X-ray, you could have pertussis pneumonia, which would explain the crackling and wheezing. If so, this is a more severe form of the disease that could place you at significant risk and might even require hospitalization. I strongly suggest that you arrange to be re-examined by your doctor, without delay, and have another chest X-ray. When you see the doctor, stress how short of breath you have been. You could be having a lot of bronchial spasm, in which case you might benefit from a long-acting bronchodilator.
Whatever the diagnosis turns out to be, you have a serious disease and, should it worsen, you should not hesitate to seek immediate assistance at the nearest Emergency Room.
Good luck
P.S. If it makes a difference, the coughing fits can sometimes last several minutes. I do cough up gunk, but it's not a particularly odd color - it doesn't look infected. My doctor heard a lot of crackling and wheezing when she listened to my lungs. My blood pressure is fine. Strangely, my throat isn't even sore. The cough seems low down at the base of my throat.