What Causes Recurrent Cough Despite Taking Claritin-D For Asthma?

I had fairly severe asthma as a child and a youth. It seemed to clear up as I became a young adult. At 53 I was having trouble with coughing all night long and spitting up white and sometimes greenish mucous. My doctor suggested that my asthma had possibly returned. She prescribed an albuterol inhaler and Claritan-D. This made a huge improvement and after a few months was able to stop with both the albuterol and the Claritan-D. Fast forward to now, 57 years old and the same symptoms have appeared, though this time it was after an upper respiratory illness that affected my wife. She got over her symptoms in a few weeks. After mine dragged on for 2 months I went to the Urgent Care. I received a regimen of antibiotics that did not seem to have an effect. Following this I went back to the routine with the albuterol and the Claritan-D. Within a few days I was significantly improved. Stayed on the Claritan-D for around 2 months and felt so good that I quit using it. I was off of it for around 2 months and the symptoms reappeared. I started back on the Claritan-D, though this time the improvement was slow to come and I cannot seem to get rid of of the cough or coughing up mucous.