I have the same problem. A while ago I discovered a company called Simply Whispers. All the earrings, etc., they sell are nickel-free--the post as well as the earring. You can get surgical steel, or gold. Their website has a nice selection of ready-made that's not too expensive, plus they offer findings if you want to make your own. Also, most sterling silver earrings have surgical steel posts. If you have a pair of earrings you want to wear just once in a while but know it will irritate you, you could try nail polish.
You can also get dangles (French hook) that are sterling for just a few dollars at craft stores (JoAnne's, Michael's, Hobby Lobby): put a bead on a pin, attach to the dangle and you're in business.
I would be cautious about buying any costume jewelry (especially from Claire's or discount stores) unless it is labeled "surgical steel posts"--even then, the part of the earring around the post that touches your ear could irritate you. Because of this problem I now buy either gold, sterling, or from Simply Whispers or else I make my own. I also find watch buying difficult for the same reason (back of the case may be nickel on cheaper watches), and now just usually end up buying sterling and wearing it forever.