Persistent cough after IMPT and chemo

HPV 16+ T2N1M0 - had effective treatment wih proton.
The one treatment side effect I have not been able to shake is a cough. Since finishing treatment at Mayo in October I have had a virtual non-stop cough. I am trying to clear gunk in my upper respiratory area 24/7. Occasionally it gets so bad that I actually vomit. Taking OTC guaifenesin and prescription benzonatate, which help somewhat.

Has anyone else had this problem? If so, what helped and did it eventually stop?

Thanks.