Every morning I cough up brown phlegm. I don't have a fever. I'm always short of breath and feel heavy in my chest. I don't smoke.

Get checked. Chest heaviness and shortness of breath in a 43yo male could implicate heart disease and you need to be checked for potential risk factors. Mucus is secreted all along the respiratory tract to catch particulates and as a barrier to infection, so some process (irritant exposure, infection, allergy, structural abnormality) is inducing its production. More info is needed to help predict cause.
See a doctor . if you are not a smoker, the see a doctor to get checked and get X-ray.