What is coughing n not being able to breathe called?

Dyspnea.....: Shortness of breath is called dyspnea. Coughing associated with difficulty breathing can be due to a multitude of disorders including acute or chronic bronchitis, copd, pneumonia, pulmonary embolism, bronchospasm, etc. Shortness of breath can be due to a life-threatening condition so see your doctor or go to the er for evaluation and treatment. If you smoke, your doc can help you quit.

Cough.: If you're coughing and short of breath, this could be one of several things: bronchitis, pneumonia, asthma, emphysema, chronic bronchitis, bronchiectasis, sinusitis, allergic rhinitis, occupational lung disease, environmental lung disease...in other words, you need a formal investigation of your symptoms.