I don't know if this will help, but I experienced similar problems for the first 3 years of my treatment.
Throughout my life my asthma was always looming around in the background, not a problem. And then one year I had surgery and boom there it was, everyday, weasy coughing and short breath. Unfortunatley I had surgery 3 times that year and the asthma just kept getting worse.
It took almost 3 years of trial and error, but we got it under controll when doc gave me Advair 250 (I think it was 250?) and Singulair, plus I have my rescue inhaler. I am doing well enought now to have dropped to the Avair 100/50, but still take the Singulair too. I also have a nebulizer at home for when I get sick or have a bad day.
I don't know if it relates, but I am also on Zyrtec and Rhinocort Aqua for allergies.
If your doc has not tried a combination of medications all at once, you may want to ask about it. Worked for me.