If I have a reaction to a heavy metal which is found in my jewelry, should I stop wearing that piece of jewelry?

Ideally, yes. However, it may not be desirable due to the sentimental value that piece of jewelry carries. You may wish to consider eliminating exposure to other heavy metals first as a starting point. 
As visually outlined below, the Toxic Bucket Theory teaches the importance of continuously monitoring, managing, and measuring the exposure of toxicity in the body and ensuring we are detoxing heavy metals from the body.