Should i work out if i'm coughing up green phlegm?

Up to you: Whether or not to continue exercising while sick is really a personal decision depending upon how you feel, not color of your phlegm. As an aside, color of phlegm doesn't determine need for antibiotics either. Bottom line, if you feel good aside from coughing up green phlegm, go exercise. But there's no need to push for a personal best/record until you're back to 100% health.