It is possible.
Your veterinarian can test your dog for these allergens and others, and have an allergy serum prepared to be used to desensitize your dog against the allergens. Desentization can be helpful in many cases, but it takes a long time to acquire a lasting response. Desentization sometimes takes a year or longer for a dog with multiple environmental allergens. Occasionally, food allergies are also involved. There is no successful desensitization technique for food allergies however, and, the only successful treatment is hypoallergenic food.
Wheezing is an unusual allergy symptom for dogs, but it can occur. Other causes include upper respiratory infections with or without allergies, and, heart disease; so please have your dog checked by your veterinarian ASAP.