If I eat eggs, I break out in hives.

Literal

Eggs [object-を] eat-if hives [subject-が] appear.

The と conditional describes an automatic or habitual consequence — 'whenever X, Y (inevitably) follows.' Perfect for describing allergies, natural laws, and reliable patterns. じんましん ('urticaria / hives') is a medical term for skin welts. 出る ('to come out / appear') is the standard verb for symptoms manifesting.