My toddler has had an allergic reaction to strawberries. How do I confirm a true allergy?

Skin test. If the reaction was severe, your child should be skin tested to strawberries and then if negative or weakly positive, openly challenged in the allergist's office in a safe manner. It is ok to simply challenge your child again only if the reaction didn't require any medical attention or medication in order to resolve.
See below. The easiest test would be to give your child strawberries again. If the reaction recurs, then likely to be allergic.