The best hypoallergenic earrings are made from precious metals such as gold, platinum or 925 silver. Make sure you buy allergy-safe earrings that are made from 14k gold or higher, or sterling silver 925, so you don't risk nickel being mixed in.
However, you may want to avoid pure 24k gold. Although it is a hypoallergenic material, unless you are allergic to even the tiniest quantities of nickel because of how soft and malleable pure 24k gold is. It easily distorts and becomes damaged from regular jewelry wear, so you definitely don't want to buy 24k gold earrings - they'll get damaged very quickly. Plus, earring prongs holding pavé stones require a tight grip; but 24k gold is an ultra soft metal. So, 24k gold jewelry lovers should expect to lose a few pavé stones eventually.
24k gold earrings are much too soft for daily jewelry wear, especially when being worn in the ear. 14k or 18k gold will give you a better option without having to worry about unsightly scratches, dents and other damage ruining your beautiful, new earrings.