Here are some highlights from a good article I found; it also describes the different metals to look for:
https://www.ebay.com/gds/How-to-Buy-the-Right-Jewelry-When-You-Have-a-Metal-Allergy
Piercings are often triggers that cause allergies due to the metal particles being exposed to open wounds. Metal allergies do not go away, and repeated exposure can worsen the condition.
Nickel is the primary metal that
people are allergic to. Jewelry pieces containing this metal are high irritants because nickel dissolves in
water and forms salts. Through sweating or washing, the salts get into the skin and cause itchy, painful reactions. Perfumes, soaps, and lotions on the skin can have the same results if there is
enough moisture. Copper and cobalt are also responsible for causing allergic reactions in some individuals.
Some people think that they are allergic to gold and silver, but these metals only cause reactions in extremely rare circumstances. The more likely culprits in these situations are the alloys that are combined with the gold or silver to make the material harder and less expensive. Low-karat gold and silver are often mixed with nickel and copper, which are the sources for many allergic reactions. Copper is also used to make brass jewelry, which some people believe they are allergic to.
Expert jewelers recommend surgical-grade stainless steel for the earring wires, posts, and findings. When shopping for earrings, look for the words "surgical" or "nickel-free" because regular steel contains nickel alloys that can cause skin reactions.
Niobium or surgical steel earring hooks are ideal for allergy sufferers.
Experiment with different hypoallergenic metals to find styles that meet individual preferences.