I too have cough-variant asthma. Every year, I have asthma flare-ups when I get a cold or sinus infection. For me, working closely with my PCP helps me find the balance between treating the infection and getting the asthma under control. Also, cold air will trigger an asthma flare-up also. Now that it is warming up, my next challenge will be the pollens and allergies that tend to trigger the asthma. If it isn't one thing, it is usually another.
Even with bad flare-ups, my doc won't give me any cough surpressents. She does encourage the Mucinex though.
Last year, I had the cough really bad for 4 months. I ended up in the doctors office 9 times. At one point, I asked her if I was being a hypochondriac and if I should just live with the cough. Her response was that there was something wrong and we just needed to find the right combination of things that would work to get it under control.
As I suffered through the bad coughing periods, I learned that there are 4 main causes of a cough like this. 1. Asthma 2. Post Nasal Drip 3. Allergies 4. Acid Reflux. When I originally thought the cough was just from PND and allergies, I was eventually tested and found to also have asthma and acid reflux. My current year-round asthma treatment: Advair 500/50, Singulair and Albuterol as needed. I also take 3 allergy meds and one for acid reflux (even though I never had any heartburn).
Talk about feeling like a drug addict. At least the cough is mostly under control year-round now. My only tough times are during bad air days in the winter and summer.
Good luck finding what works for you.