I agree with Cheryl O. - I had ALL of these happen to me until I was diagnosed and on allergy meds and shots: multiple sinus infections each year that always led to an ear infection, bronchitis almost every year, and pneumonia twice. It's a miracle I didn't end up with some "super bug" due to all the antibiotics I was always on. This was all before my 9th birthday.
When I started allergy meds (they weren't highly available OTC like they are now) it was a whole new world. I could play at my friends houses who had cats and dogs for a few hours without being miserable the whole time, we had a bunny as an outdoor pet that I could pet and hold, and my illnesses were less often and less severe.
My son clearly had allergies and by age three the sneezing and coughing was actually causing him to lose several hours of sleep per night, making him a total nightmare of a toddler. Put him on a half dose of zyrtec once a D. (the full dose the Dr reccommended was making him groggy and weird), and he actually starting sleeping three extra hours per night!! He was a whole new kid, and we could actually see his beautiful blue eyes when he woke up because his eyes weren't all puffed up :)
This year in first grade he was coming home from school with bloodshot eyes, and I thought he was allergic to something in his classroom. We had a physical done, and he pretty much failed the quickie eye exam. Turns out he needs glasses, and they arrive next week.
Go to the doctor ALL together, see what (s)he has to say and prod your husband to ask as many questions as he needs to. We are not big on meds in our house either; I don't give tylenol for a fever, I let the fever do it's work. I don't take meds for headaches until I've tried rehydrating, napping and other things that could be the cause. But when it comes to allergies... we have anti allergy covers on beds and pillows, we have hardwood floors that are regularly mopped and no stuffed animals on the bed, we run a humidifier 24/7, and keep fans dusted and clean and my son STILL can't go a D. without his zyrtec!
Hopefully hearing other people's experience with allergies, and a doctors knowledge - maybe even get a referral to an allergist, if their expertise will help convince your husband - will help bring your husband around. Living with untreated allergies SUCKS.