My experience is similar to yours and I've been on 300mg Dupixent injections for about 1.5 years.
I was diagnosed at Mayo clinic Rochester Mn. in 2014 after 7 years of steroid injections and two sinus surgeries. Diagnosis: Aspirin exacerbated respiratory disease. (AERD) Also known as Samter's triad: Asthma, Nasal Polyps, Sinusitis.
All allergy tests were negative at two different Allergist's.
However; a integrative health specialist found I had food intolerances on top of the AERD. So I can not have Gluten, Soy, Corn, fermented foods or alcoholic beverages. No beer unless certified "Gluten free". Ingesting these foods causes: asthma typical reaction, runny nose and or post nasal drip, especially at night if I have accidently been contaminated at a restaurant.
Dupixent has been wonderful, however, about 6 months ago, some of the symptoms are returning. Voice impairment, post nasal, caugh. I do use Budesonide, sea salt sinus rinses that help with post nasal. (Squeeze bottle works best).
You might request an Aspirin challenge for AERD. Also, see a doctor that tests for food intolerances, which is different than an allergy.
Best of luck and hope this helps determine cause of your issues.