Fatigue. Hot flashes. Thinning hair. The nagging feeling that something just wasn’t right.

In 2010, Kimberly Hill began experiencing these symptoms, so she turned to doctors in her hometown of Knoxville, Tenn. They diagnosed the mother of three with thyroid cancer. Kimberly, who was 40 at the time, underwent a thyroidectomy and radical neck surgeries for treatment.

But years later, the symptoms wouldn’t go away. In fact,...