There are no essential carbohydrates. Nobody needs sugar in any form to survive.
That being said, it's damned tasty.
Please be clear that there are many types of sugar and they all have different effects in the body, okay? The sugar in fruit and the sugar on your table have, for the most part, the same split between glucose and fructose.
And it's not possible to have an allergy to sugar. You can have trouble digesting it or metabolizing it though.