(CNN) The second Dallas health care worker who was found to have the Ebola virus should not have boarded a commercial jet Monday, health officials say.

Because she had helped care for Ebola patient Thomas Eric Duncan, and because another health worker who cared for Duncan had been diagnosed with Ebola, the worker was not allowed to travel on a commercial plane with other people, said Dr. Tom Frieden, director of the Centers for Disease Control and Prevention.

The worker had a temperature of 99.5 Fahrenheit (37.5 Celsius) before she boarded her flight, he added.

Health care workers who had been exposed to Duncan were undergoing self-monitoring. They were allowed to travel but not on a commercial plane with other people, Frieden said.

Moving forward, the CDC will ensure that no one else in such a situation travels outside of a closed environment, he said.

The worker is Amber Vinson, 29, a nurse at Texas Health Presbyterian Hospital in Dallas. She was confirmed to have Ebola overnight. Now, she will be transferred from the Dallas hospital to Emory University Hospital in Atlanta, which has successfully treated two other patients. It is now treating a third: a male health care worker who was infected in Sierra Leone.

Vinson is "ill but clinically stable," Frieden said.

The first Dallas health care worker with Ebola, Nina Pham, is in "improved condition," Frieden said. It has not been determined whether she will be transferred to another facility.

Both Dallas health workers had "extensive contact" with Duncan on October 28-30, when he had "extensive production of body fluids" such as vomit and diarrhea, Frieden told reporters in a conference call.

CDC wants to interview passengers

The risk of exposure to the passengers who were on the plane with Vinson is low, since she did not yet have symptoms, health officials said Wednesday. The Ebola virus is not contagious before symptoms set in.

Still, the CDC wants to interview all 132 passengers who were on the plane with her.

"Because of the proximity in time between the evening flight and first report of illness the following morning, CDC is reaching out to passengers who flew on Frontier Airlines flight 1143 Cleveland to Dallas/Fort Worth Oct. 13," the CDC said in a statement. The flight landed Monday at 8:16 p.m. CT.

The woman "exhibited no symptoms or sign of illness while on Flight 1143, according to the crew," Frontier Airlines said in a statement.

Earlier, Vinson flew from Dallas-Fort Worth to Cleveland on Frontier Flight 1142 on October 10.

The airline said customers who may have traveled on either flight should contact the CDC at 1-800-CDC-INFO (1-800-232-4636). But the CDC statement, contained in the same news release, said the CDC wanted to speak only with passengers of the October 13 flight. The CDC later confirmed to CNN that it is "only interested" in the passengers on Flight 1143.

The October 13 flight was cleaned thoroughly after it landed, "per our normal procedures which is consistent with CDC guidelines," the airline said. After the airline was informed of the Ebola patient, the plane was removed from service.

In a sign of growing concerns about Ebola, President Obama canceled trips to New Jersey and Connecticut on Wednesday to convene a meeting at the White House of Cabinet agencies coordinating the government's response to the outbreak.

Hospital denies 'institutional problem'

Vinson, who lives alone, is in isolation at Texas Health Presbyterian Hospital.

The news that she contracted Ebola cast further doubt on the hospital's ability to handle the virus and protect employees.

It's the same hospital that initially sent Thomas Eric Duncan home, even though he had a fever and had traveled from West Africa. By the time he returned to the hospital, his symptoms had worsened. He died while being treated by medical staff, including the two women who have now contracted the disease.

"I don't think we have a systematic institutional problem," Dr. Daniel Varga, chief clinical officer of Texas Health Resources, told reporters Wednesday, facing questions about the hospital's actions.

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Medical staff "may have done some things differently with the benefit of what we know today," he said, adding, "no one wants to get this right more than our hospital."

People in the health care worker's office building were informed when officials went door to door, and also through early morning reverse 911 calls, officials said.

The health care worker had no pets, authorities said.

More than 120 being monitored

Seventy-five health care workers in Dallas are being monitored for any Ebola symptoms, Varga said.

Separately, Dallas County Judge Clay Jenkins, who is overseeing the response efforts, said 48 other people in the community still are being monitored after having contact with Duncan, who was Dallas' first Ebola patient. Those 48 are asymptomatic, and Sunday will mark the end of the window in which they could get sick.

The second worker reported a fever Tuesday and was immediately isolated, health department spokeswoman Carrie Williams said. The virus is not contagious before there are symptoms.

A preliminary Ebola test was done late Tuesday at the state public health laboratory in Austin, and the results came back around midnight. A second test will be conducted by the Centers for Disease Control and Prevention in Atlanta.

"Health officials have interviewed the latest patient to quickly identify any contacts or potential exposures, and those people will be monitored," the health department said.

The worker's apartment and car will be cleaned Wednesday, Dallas Mayor Mike Rawlings said.

Official: Duncan should have been moved

An official close to the situation says that in hindsight, Duncan should have been transferred immediately to either Emory University Hospital in Atlanta or Nebraska Medical Center in Omaha.

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Those hospitals are among only four in the country that have biocontainment units and have been preparing for years to treat a highly infectious disease like Ebola.

"If we knew then what we know now about this hospital's ability to safely care for these patients, then we would have transferred him to Emory or Nebraska," the official told CNN senior medical correspondent Elizabeth Cohen.

"I think there are hospitals that are more than ready, but I think there are some that are not."

Troubling allegations

Also Tuesday, National Nurses United made troubling allegations about the hospital, claiming "guidelines were constantly changing" and "there were no protocols" about how to deal with the deadly virus."

"The protocols that should have been in place in Dallas were not in place, and that those protocols are not in place anywhere in the United States as far as we can tell," NNU Executive Director RoseAnn DeMoro said. "We're deeply alarmed."

Nurses were told to wrap their necks with medical tape when equipment left their necks exposed; they felt unsupported and unprepared, and they received no hands-on training, union co-president Deborah Burger said.

A Texas Health Presbyterian spokesman did not respond to the specific allegations but said patient and employee safety is the hospital's top priority.

Global epidemic

While the Texas hospital deals with its third Ebola patient, the situation in West Africa is getting increasingly dire.

A total of 4,493 people are confirmed to have died from Ebola this year, from Guinea, Liberia, Nigeria, Senegal, Sierra Leone, Spain and the United States, the World Health Organization said Wednesday.

There could be 10,000 new Ebola cases per week in Sierra Leone, Liberia and Guinea by the end of this year as the outbreak spreads, the WHO warned Tuesday.