It's not only human-added planting changes that have occurred as climate zones have changed. Existing plants are an issue. A lot of people with allergies are allergic to grasses and trees, and those may not be flowering plants. They'll keep producing pollen as long as they can, not for a set timed cycle. (For a lot flowering plants, making a flower is the end of their efforts.) Current weather patterns - especially in the Pacific Northwest - have meant a longer spring. That in turn means a longer allergy season.
Not only that, people may not intentionally plant some species, but weeds may instead move on the wind and grow in areas where temperatures or water conditions previously prevented them. So they become invasive plant species because they really don't belong in the area (watch out for them, they'll bring new insects to your garden), and yeah, people may develop allergies to them.
Climate change is definitely affecting allergy sufferers.