Recently suffered with a cold, the cough I have had for 7 days now. Coughing up green phlegm with blood and coughing when exhaling, pain in chest?

More than cold. What you described is more than a cold. Is is possible that you a mild form of pneumonia and it would be prudent to see your doctor. It is not feasible to provide a more meaningful opinion without examining you. Wish you good health!