About one month ago, I was offered an unsolicited test by Quest, and separately by the VA.
During a previous discussion with my primary physician, he said tests only with symptoms. He also said antibody tests have high error rate. Therefore they can give false sense of immunity, and therefore encourage unsafe behavior.
I get my temperature taken every 2-3 days at physical therapy. So I'll use them and symptoms as my initial screen, unless a physician directs me otherwise.