They are either the allergic items or the trigger. Either way, eliminating these 3 things can really make your animal healthier and much more comfortable. I personally feed my 2 cats and 2 dogs a completely raw and species-specific diet every day. Something else to think about if you suspect the allergies are inhalant is to install an air purifier in your house. Different forms of medicine such as homeopathy, Ayurveda and Chinese medicine may really help too - check to see if there are any good practitioners in your area.
Antioxidants are SO important.
A raw diet contains many of these, but supplementing the diet can also help. Vitamin C and E are two very well known antioxidants. Minerals like selenium and zinc boost the immune system too. Check with a doctor about proper supplementation, or simply includelots of foods that contain natural selenium and zinc. Flavonoids are found in many things, such as grape seed extract, pine bark extract, green tea and Gingko biloba.