Can a dry cough for a three week old be due to reflux even if he breast fed?

Possibly,but: In my experience this is more often related to environmental issues.House dust, fragrances,smoke, etc.all can trigger cough in small infants. Removing these irritants from there environment can often help. It is sad, but the nice flowery fragrance of the baby room or bath water can act in this way. Their little noses and lungs don't respond to these the way you do.