Chronic "tickle" when inhaling that results in a single cough

I often get a "tickle" on inhalation in the back of my throat that then causes me to start coughing. It never feels as though it is actually coming from somewhere deep in my lungs and it isn't productive. My doctor says I have columnar bronchiectasis as well as asthma. Would this tickle be related to my asthma? I really don't have a good grasp of what the differences are between the two other than if I wheeze, I assume it is my asthma. I have been diagnosed for many years and on the same meds for well over 20 years. Spiriva Respimat 2 puffs once a day, Proair HFA up to 2 puffs as needed, Advair Diskus 250/50 1 inhalation twice a day and then of course albuterol and saline nebs. More and more I am leaning towards a visit to either Mayo or Cleveland clinic down here in Florida for a second opinion. I know there have been many advances in medication. I am inconsistent with twice a day nebs because many days there is no mucous afterwards and then on days I don't do it I can become quite active. It is frustrating. I've said it before, my doctors is not interested in finding out if my bronchiectasis is MAC related because at age 77, he says I am too old and too frail and wouldn't be successful on the treatment. I think that is my decision to make not his. I don't think there are any better choices than him locally. JUST SO FRUSTRATED!! Life just keeps getting more and more limited.