Maria Estrella has been waiting for her Covid-19 test results since March 17. The South Florida resident began feeling ill, with a sore throat, fever and headache, after returning from a trip to northern Italy. When she was tested at the Mercy Miami Hospital emergency room, staff said the results were sent to a private lab in Georgia and would take three to six days.

Ms. Estrella’s symptoms have subsided, and she has returned home, but the uncertainty continues to disrupt her life. Her husband, who has displayed no signs...