If your skin is super sensitive, you may only be able to safely wear solid gold. However, if your jewelry happens to be made from nickel, take it to a jeweler and have them plate it with platinum, which is naturally hypoallergenic.
You definitely shouldn't wear the fake stuff if you know you’re allergic to lower-quality metals. Costume jewelry is notorious for using nickel, which causes more skin reactions for people than any other metal.
Top dermatologists recommend 1% hydrocortisone ointment as the best form of treatment. However, avoid creams at first, as it could exacerbate your skin issue. Once your skin is soothed, you can move on to steroids and emollient creams.