You seem to be suffering from viral upper respiratory tract infection which is a common type of throat infection in this season. Forceful coughing can sometimes cause rupture of small blood vessels of airway leading to minor bleeding. You may need to take antibiotics, cough syrups and steam inhalation for faster recovery

Blood in sputum from cough is to be evaluated by ENT specialist ASAP There could be a severe throat infection or ulcer in your throat or a lung infection . Different conditions cause blood in sputum from cough medically it is termed as " Hemoptysis " In India Tuberculosis is again very prevalent and so you need to consult a ENT specialist ASAP to identify the cause of blood in sputum during cough don't ignore your symptoms.