You can be allergic to specific ingredients within the ice cream, such as dairy, nuts, wheat/gluten, or soy. All US ice cream labels should carry allergen information.
You can have an allergy to anything, including ice cream. Many people are lactose intolerant, which basically makes them allergic to all dairy products.
It is possible to have an allergy to ice cream if you are lactose intolerant. Check for other ice creams available at your grocers, especially for those with this allergy.
