I've had a very sore throat for the past 3 days and have been spitting up phlem, but half the time there's blood or red/brown flakes. is that serious?

Unlikely: Likely inflammation in the airway with small blood flecks from excessive coughing. Usual therapy is narcotic cough rx ie Codeine and steroids with abs for significant fever. If symptoms do not improve, tou need x-rays and possible bronchoscopy.

Epistaxis: Have it checked anyway to make sure. By your symptoms you have upper respiratory infection or inflammation. The mucous dries up the superficial vessels from the kisselbach's plexus to the back of the throat, they pop and get mixed with the secretions especially in the morning. It still could be from the lungs although less likely. It is best to see your doctor for evaluation.