Cigarette and Cigar Smoke
These days, you're most apt to encounter tobacco smoke outdoors. Depending on your city's rules, you may still have to fend with cigarette smoke at restaurants and other communal businesses. Opt for a non-smoking section, or even consider lobbying your local government to adopt ordinances designating your city smoke-free.
The trick to avoiding pollen is knowing when it's most prevalent. At the height of the pollen season, you should stay inside during early morning hours, from 5-10 AM -- or travel to a pollen-free region for the duration. Otherwise, take simple actions such as keeping your car windows closed while driving, and staying indoors on windy and humid days.
The real reason dust tends to trigger allergies is because there are creatures that feed on it, called dust mites. Reduce the presence of dust mites in your home by using a dehumidifier to keep the air dry, and vacuum and dust your house weekly. The bedroom is a major center for dust mites; encase your mattress in plastic or an allergen-proof fabric cover to keep them out.
Unfortunately, there's no easy solution if your child is allergic to the pet you already have - it's a losing battle trying to keep up with your animal's dander. However, if you're on the hunt for a new pet, you may find that certain breeds of cat or dog cause less of a reaction in your child. Spend time with prospective pets before taking them home, if you can.
Perfumes and Colognes
People who are sensitive to the fragrances found in perfumes and colognes are likely to find their sensitivity getting worse over time. The best way to prevent your child from suffering from fragrance irritation is to refrain from using perfumes yourself, and let the adults your child interacts with know about the problem. They'll probably be happy to do what they can to help out.
You can't do a lot about the air quality outside your home, but there's a lot you can do to control the air quality inside. Keep your home clean and well ventilated, and regulate the humidity with a dehumidifier. You can also purchase air filtration systems that remove airborne irritants; these systems require only an occasional cleaning.
Mold is a serious health hazard, and its allergens are only the beginning. It's critical to remove mold wherever you find it, which is usually in damp areas such as bathrooms and basements. For minor cases, cleaning the affected areas with a bleach solution should be sufficient. For a major mold infestation, you may need to get professional help.