Coughing up colored sputum is a sign of infection. I, also, have asthma
and tend to get
bronchitis very easily after I've been sick, even with a cold or flu.
Are you currently seeing a pulmonologist or strictly your primary care physician? If you are not seeing a pulmonary doc, I strongly advise you to get in to see one. They can definitely do more testing to see exactly what is going on and if, in fact, this is a case of chronic bronchitis, which is sometimes seen in COPD.