Is watermelon a common trigger for allergies?

Possibly. There is something called oral allergy syndrome, where people who are allergic to ragweed, cannot eat the melon family. They get itching in the mouth and ears, and sometimes swelling. This occurs in people who are allergic to birch trees, and eat hazelnuts, or some fruits such as apple, plums, and nectarines.
Not really. Watermelon is not really a "common" allergen, although watermelon and other melons often cause oral itching/rash in patients with severe allergy to ragweed pollen. This is called oral allergy syndrome.