I had cough variant asthma for many years (Way before there were any treatments that we have today!!) It took a long time to pinpoint this down as it was in the 70s and 80s. I have asthma - unfortunately controlled with Prednisone for many years, and take Dupixent every other week. Please ask about the following:
Can you take an antihistamine - such as Chlortimeton (chlorphenamine maleate) mild antihistamine and helps with post-nasal drip. I only need 1 tab am/pm instead of 4 as listed on the box. Guifessen is not always a good choice for asthmatics - as it can make many worse in their symptoms. Cough/cold remedies which have dextromethorphan can be helpful. When the wheezing happens from the cough variant asthma, it is usually high up in the lungs, causing air trapping lower in the lungs. Possibly consider a biologic - possibly Xolair - which is now used for severe allergic reactions, or one of the others. Disclaimer - I am not affiliated with any pharmaceutical company. I have asthma in many different forms for about 60 years. Good luck!