What Causes Muscle Strain While Suffering From Cough?

I have had a cough for the last 2 weeks. It initially started with a high fever for one day, and by the next day i could feel the pressure in my chest. The cough got worse and worse, I was coughing up dark green phlegm, I couldn t even walk anywhere without having trouble breathing or talking. I did not feel that sick, just extremely exhausted .i went to the doctor and was put on antibiotics. I finished my round of antibiotics and the cough is still there, a bit less severe though. Today I woke up and the middle of my neck was extremely painful to touch (It hurts where the cartilage is of my wind pipe/adams apple) Is this caused by the excessive coughing and is a muscle strain, or could it be from whatever infection I seem to have?