If you're one of the many people who have a hard time wearing jewelry due to irritation, you probably have a metal allergy. The metal culprit is usually nickel, which is used as an alloy for many metals.
Some options are:
Don't wear your jewelry for extended periods of time
Put a few coats of clear nailpolish or Allergy Jewelry Shield to the jewelry that touches your skin
Wear 14k gold, medical-grade titanium, argentinum silver, fine silver or niobium.
It may take some experimenting to see which metals are most comfortable for you. Most people don't have a problem with sterling silver or 14k gold-filled. If you are sensitive, you might want to avoid plated items (like vermeil, unless it is specified to be nickel-free).
If you'd like to swap earwires on my designs, email me and I can quote you a price depending on what option you'd like. In the image above, the top row are niobium earwires while the bottom row are 14k gold earwire options.