The pain in the ribcage when coughing is most likely related to the increased sensitiveness of the diaphragm. It is possible that it might even initiate the gagging and the vomiting reflex you experienced via the mutual inervation from the vagus nerve.
It is also possible that the feeling that you lose your breath when coughing is due to the repetitive cough which does not allow you to inhale.
As you see, all you experienced is likely normal for bronchitis. Your form of bronchitis seems to be rather severe and, therefore, the symptoms might seem a little frightening.
You might want to consult with your doctor about taking anti-cough over-the-counter products if there is no mucus in the lungs. If secretions are present, taking products that reduce the cough might decrease the removal of the mucus. The mucus that might be left in the lungs might be an excellent environment for multiplying bacteria.
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