Never wear ear-rings owned by somebody else without sterilising them. If a shop lets you try ear-rings before purchase, don't buy from them. Reputable shops may sell secondhand ear-rings as we do. Before reselling we always sterilize by boiling for at least 10 minutes. If this would damage the stones, we either have the stones removed, or simply won't sell the ear-rings.
Some people are allergic to certain metals, often nickel.
Most allergic reactions are to cheaper costume ear-rings, although on rare occasions gold and silver can cause a reaction. You can't overcome an allergy by fighting it. With continued exposure you may well make the allergy worse. So don't wear those ear-rings again. If they are drop ear-rings, ask a jeweller to change the post which passes through you ears to a metal which doesn't affect you.