Fungal infections in the sinuses are often responsible for chronic sinus issues (including post nasal drip).
Fungal lung/airway infections (Aspergillus is a common one in those with Asthma) may need to be treated for you to find relief.
Also, my DH and I both had more Asthma troubles when we had mold growing in our house. After getting rid of the mold, my allergies are a fraction of the severity they were before, and my DH's Asthma is under much better control.
Finally, Vitamin D deficiency can cause steroids to not work for allergies. Consider asking your Allergist or Primary Care doctor to test your Vitamin D3 level...
Chronic Lyme, Bart., Gluten & Sulfite Sensitivity, Many Food/Inhalant/Medication/Chemical Allergies & Intolerances, Asthma, Gut dysmotility & non-specific inflammation, Lupus, Osteoporosis, etc.; G-Tube; TPN-dependent
Meds: Zofran, Domperidone, Hydrocortisone, Essential Oils, Homeopathy, Herbs, etc.