Before buying any silver earrings, you need to check the material used in the same. For instance - higher the nickel count in the same can lead to nickel itch. On the other hand, sterling silver rarely causes any form of irritation and is a bit pricey.
However, if your favourite pair of earrings cause an itch and you do not have a budget to buy a good one, then it is best to use a coating of clear enamel or clear nail paint. The same will do the trick. However, if the infection persists, it is best to discard these.