Is it possible to have an allergy to grapes?

It is possible to have an allergy to just about anything, so the answer is yes.

There are several special problems about grapes worth noting:

1. They are heavily sprayed with pesticides, making them the most toxic fruit you can buy.
2. Grapes naturally grow yeast on their skin.
3. Like any fruit, mold can grow on grapes.

Rather than a grape allergy, you may instead be allergic to pesticides, yeast or mold.