Health experts have been worrying about a third wave of COVID-19 hitting the U.S. after the holidays, as already 9 million people have traveled during the season. But speaking to "Good Morning America" Monday morning, Adm. Brett Giroir, the assistant secretary for health at the U.S. Department of Health and Human Services (HHS), said the country may not see another big spike in cases.

"How bad it will get really depends on what people do. After Thanksgiving, in the Midwest and the Northern Plains, we did not see a spike in cases, and in fact, it continued to go down," he said.

He added that while traveling does put people at higher risk of contracting the disease, we will not necessarily see another spike if people follow the rules.

"Limit travel if you can. If you're sick, please don't travel. Always wear a mask and watch your distance. And be careful, it's not really the travel, but it's mixing your bubble with a new bubble once you get there," Giroir said.

He added that this week, 4.7 million doses of a COVID-19 vaccine will be delivered to the U.S., getting the country closer to the government's goal of vaccinating 20 million Americans by the end of the year.

Adm. Brett Giroir, the assistant secretary for health at the U.S. Department of Health and Human Services (HHS) spoke to "Good Morning America" Monday morning to discuss the new coronavirus variant taking over the U.K.

"We don't have proof that it's here, but we do suspect that it is likely here, given the global interconnectedness," Giroir said. "We have no evidence that it's here. It's certainly not widespread here, but we need to look and make sure it's not here."

He added that while "there is increasing evidence that it really is more transmissible" or contagious, due to the viral load that people with that strain have been shown to have, there is "no evidence that it is more serious."

There is no evidence that people who become infected with the variant are more likely to be hospitalized or die, Giroir said.

"And we still believe -- don't have absolute proof -- but we have very good evidence and a good belief that the vaccines will still be effective," he added.

Huntington Hospital in Pasadena, California, released a patient information sheet documenting how they will use their medical resources should they see a shortage due to an overwhelming number of new patients following the holidays.

"We are not currently in this situation, but could be based on ongoing increase in hospitalized COVID-19 patients," they told ABC News, adding that on Sunday they had their highest number of patients (189) in a single day.

In the letter, the hospital explained that due to rising cases of COVID-19 in the community, they may experience limited resources. These include life support machines (like a ventilator or breathing machine), intensive care unit (ICU) beds and healthy medical staff to care for patients.

If there is a shortage of resources, a team of medical professionals will review the cases of all patients who are critically ill to determine how these resources should be shared throughout the hospital.

"If a patient becomes extremely sick and very unlikely to survive his/her illness (even with life-saving treatment) – limited medical resources may go to treat other patients who are more likely to survive," the letter reads.

"Our community is facing a public health emergency that has severely constricted the medical resources available to patients in the Los Angeles County and greater Southern California region. Hospitals such as ours are working hard to meet the dramatic rise in needed care during this COVID-19 surge. We expect to face additional challenges moving forward after the holiday season," the hospital said in a statement.

ABC News' Abigail Shalawylo contributed to this report.

The Centers for Disease Control and Prevention updated its guidelines for people with underlying health conditions planning to take a COVID-19 vaccine.

They CDC said that adults with underlying medical conditions -- who are more at risk of becoming seriously ill from COVID-19 -- can receive a vaccine against the virus as long as they have not had a severe allergic reaction to any of the ingredients in it.

The new guidelines state that people with HIV and those with weakened immune systems due to other illnesses or medication should be aware that information about the safety of COVID-19 vaccines for their group is not yet available. While people with HIV were included in clinical trials, more data is required to provide safety guidelines regarding the effects a vaccine could have on them. The same is true for people with autoimmune conditions.

People who have previously had Guillain-Barre syndrome or Bell’s palsy may receive a COVID-19 vaccine, though experts are still acquiring more data about their groups as well.

The CDC added that people should continue to follow coronavirus health measures -- such as wearing a mask and staying 6 feet away from others -- after receiving the shot, as experts have more to learn about the protection that COVID-19 vaccines provide under real-life conditions.

Public Health England does not recommend mixing COVID-19 vaccines from different suppliers, according to the agency's head of immunizations, Dr. Mary Ramsay.

"We do not recommend mixing the COVID-19 vaccines -- if your first dose is the Pfizer vaccine you should not be given the AstraZeneca vaccine for your second dose and vice versa," Ramsay said in a statement Saturday. "There may be extremely rare occasions where the same vaccine is not available, or where it is not known what vaccine the patient received. Every effort should be made to give them the same vaccine, but where this is not possible it is better to give a second dose of another vaccine than not at all."

The clarification comes amid questions over the British government's updated guidance on COVID-19 vaccines, which now says that if individuals who received the first shot go to an immunization site where that same vaccine is not available for a second shot, or if the first vaccine received is unknown, "it is reasonable to offer one dose of the locally available product to complete the schedule."

"This option is preferred if the individual is likely to be at immediate high risk or is considered unlikely to attend again," the guidance adds.

The guidance, which was updated Thursday, also notes that "there is no evidence on the interchangeability of the COVID-19 vaccines although studies are underway," and thus "every effort should be made to determine which vaccine the individual received and to complete with the same vaccine."

Next week, the United Kingdom is set to begin distribution of a COVID-19 vaccine developed by England's University of Oxford and manufactured by British-Swedish pharmaceutical giant AstraZeneca, after the drug was approved Wednesday for emergency supply. Another COVID-19 vaccine developed by U.S. pharmaceutical giant Pfizer and its German partner BioNTech was approved in the U.K. on Dec. 2 and rollout began a week later.

ABC News' Zoe Magee contributed to this report.