Asthma with cough

About a month ago I had a mild respiratory infection. I did two rounds of Antibiotics and my mild low grade fever went away. I felt better. However, I am still coughing. My doctor called in extra Dulera (corticosteroid) to take twice daily versus once daily before. I have been coughing daily though. I am out of shape and have been trying to do extra walking each day but any more than that and I cough a lot more. Anyone have allergic and exercise induced asthma with cough? I usually have this cough for 3 to 6 months out of the year. Everyone thinks I'm sick at work all the time, I would really love to get rid of this thing!! Anyone else have this too? Tweet