Did anyone ruled out Gerd? My astham/allergy md herself takes anti-gerd medicine.
Are you using netty pot ? - strongly suggest or need to rule out post nasal drain.
I bet your ribs and diaphragm hurts like crazy. If yes, try massage therapist who knows how to release intercostal pain/tightness or chiro.

Back to cough, are you on any around the clock inhalers for maintenance like advair hfa?

If you never tried nebulizer, please try. For most people with asthma nebulized albuterol works better or different then puffs.

I also asked my pulm md for atrovent and i put it together with albuterol in nebulizer (this is the mix of two meds used in our ed). So i do it at home. When i have it bad, it can be every 2-3 hours, but Atrovent helps to relax smooth muscles and stop the cough. Could be weeks before it gets better at least for me. I also see Eastern medicine doctor: herbs, cupping, ear seeds, acupuncture.
Thanks
Lena