It's called "air hunger" (technical term: "dyspnea") and may be a symptom of a wide variety of issues.
Try to get on something for the sinus symptoms and see if that helps. If not, If I were you, I'd be persistant in seeking an answer for the cause of the "air hunger."
Chronic Lyme, Bart., Gluten & Sulfite Sensitivity, Many Food/Inhalant/Medication/Chemical Allergies & Intolerances, Asthma, Gut dysmotility & non-specific inflammation, UCTD, Osteoporosis, etc.; G-Tube
Meds: Cipro, Claritin, Domperidone, nutritional supplements, homeopathy, probiotics, etc.