Allergy or ring rash?
A red, itchy patch under a ring is often not an allergy at all. Soap, hand cream and moisture trapped under the band can irritate the skin, especially under wider rings. It is sometimes called wedding ring rash.
Take the ring off to wash your hands, dry the skin and the inside of the ring thoroughly, and clean the ring regularly. If the irritation fades, that was the cause.
A true metal allergy is usually a reaction to nickel, which is present in some white gold alloys. If the irritation persists, see your GP or a pharmacist, and tell your jeweller.