Raquel Iacurto went to sleep with a bad headache last Tuesday.

The next day, she said, “I had some tightness in my chest, and really bad body aches.” She called in sick at work and went to an urgent-care center, where she tested negative for the flu and was sent home to her apartment in Valley Stream, N.Y.

That night, Ms. Iacurto woke up…

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