DALLAS — New shortcomings emerged Wednesday in the nation’s response to the Ebola virus after it was revealed that a second nurse was infected with Ebola at a hospital here and that she had traveled on a commercial flight the day before she showed symptoms of the disease.

The nurse, Amber Joy Vinson, 29, was on the medical team that cared for the Ebola victim Thomas Eric Duncan after he was admitted to the hospital on Sept. 28 and put in isolation. Ms. Vinson should not have traveled on a commercial flight, the director of the federal Centers for Disease Control and Prevention said after learning that she was a passenger on Frontier Airlines Flight 1143 on Monday, flying from Cleveland to Dallas-Fort Worth.

But hours after the director, Dr. Thomas R. Frieden, made that statement, one official said that Ms. Vinson had indeed called the C.D.C. before boarding the plane, but was allowed to fly because she barely had a fever.