Allergies can and frequently do develop in adulthood. In fact, it often does take several years to develop new allergies, as the allergen needs to stimulate production of antibodies, and this can take several rounds of exposure before enough antibodies form to lead to significant allergies. So, for example, in year one your body responds to a new allergen (tree pollen) by making some antibodies, and some memory B-cells (the cells that produce antibodies). The following year, the memory B-cell population expands in response to more tree pollen, but the antibodies produced don’t cause symptoms. Then, in the 3rd year, enough antibodies are made to lead to symptomatic allergies, and every year thereafter you may suffer, depending on the seasonal variation in allergen production.
Obviously, this was just an example. Each person’s time course may vary for a number of reasons. But, in summary, many people develop allergies in adulthood (I did…)