What Causes Constant Irritation In The Throat Despite Taking Prednisone?

Recently was given a short 9 day cource of prednisone for suspected asthma , have had allergies all of my life environmental plus wasps, 2 more days left , but at night am still experiencing some irritation , I can tell it s not completely gone , what does this mean , was the medicine not strong enough? I was given 5 milligrams 8 pills for three days and then 6 pills for three days and now my last few days of four pills, it has helped I m not coughing uncontrollably now but there s still irritation in my throat and I can feel something not quite right in my lungs , very frustrating , ps it seems my trip to India Dehli the pollution there , it started when I returned from there but I coughed the entire three weeks I was there , it was so toxic there