Allergies can develop even after years of not having them, so maybe it's not that the climate has changed so much to trigger them - it's more likely that your body has started reacting to pollen for other reasons. Repeated exposure over time, stress, changes in your immune system, even moving to an area with more allergenic trees... all of that plays a role.
That said, yes, trees actually do flower earlier than they did a few decades ago, and pollen seasons are longer in many places. But what we experience firsthand (like the fact that sneezing was worse this year than last year) depends on so many variables: local weather conditions of that particular spring, humidity, temperatures. Maybe it's a combination - your body became sensitive, and at the same time the environmental situation got bad for you too. Have you tried monitoring whether your symptoms are worse in certain weeks or after windy days?