While not common (some experts say it is not possible) it seems there are some people who are allergic to sugar, or have symptoms very like allergies to various forms of sugars. I know my mother was highly allergic to honey, which is also not all that common. Of course, many people are allergic to grains, especially gluten grains, which might appear to be an allergy to sugar, when the allergy is really the foundation the sugar may be laid upon.
As with many allergies, people often strangely crave the very thing that cause them problems. Why, no one seems to know. Here are a few studies I found relating to sugar allergies: