What causes cough with a stabbing pain in lower left back?

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A productive cough associated with shortness of breath and chest pain always indicates a need for clinical examination and appropriate special investigations as follows.Clinical examination with auscultation (using a stethoscope), Chest x-ray, Sputum specimen for culture, Oxygen saturation, Basic blood tests. Based on these results your doctor will know if you have a bacterial or a viral infection and will decide on treatment with or without antibiotics respectively. He will also decide if you could be treated while resting at home or need in-hospital treatment. When an acute respiratory tract infection has been excluded you would be investigated for the less common causes of your symptoms. If you were known for having asthma, then acute asthma exacerbation would replace common acute respiratory tract infection as the most likely cause. The most common cause of a persistent cough in someone of your age and body habitus would most certainly be an acute respiratory tract infection. Acute respiratory tract infection resulting from viral influenza is common in the winter, whereas bacterial bronchitis and pneumonia occur all round the year. The color of sputum is not a reliable evidence to distinguish between viral and bacterial pathogens. So, I suggest you visit your doctor and get a physical and clinical evaluation done as soon as possible, as it can progress and lead to unnecessary complications.