For about a week I have what seems like dry cough during day & in the mornings I have more cough with thick green mucus. Why? Dr only says it is viral

? Sinusitis . Can start as viral, then bacteria would kick in later causing secondary infection and lingering symptoms as what you described, you want to see your doctor again for re-evaluation or seek a second opnion, it's your right, as you may need antibiotics.