Is it worth it to allergy test (skin prick) a 3 month baby?

Depends: It would depend on the clinical symptoms or reaction which your child has/had. For example, it can be useful in severe eczematous patients as studies range in a 30-50% rate of a food allergy which could potentially be triggering/contributing to your child's eczema. This should be discussed in detail with your child's allergy specialist.

No : Morse likely skin testing at this young age will not be helpful at all. We start allergy skin testif by the age of 2-3 years.

I wouldn't: The important allergic triggers at this age can be defined through blood testing.