For some children, that could mean five or six shots in a single visit, but it's safe to do so, doctors told ABC News.
"You can't overwhelm the immune system with these vaccines," said Dr. Margaret Fisher, a pediatric infectious disease specialist in New Jersey and chair of the AAP Global Immunization Advocacy Project.
Autumn is often less hectic at pediatricians' offices, which is serendipitous for parents looking to schedule COVID-19 vaccine appointments.
"We're kind of in a sweet spot," said Dr. Natasha Burgert, a pediatric specialist in Kansas, with most children flooding doctors offices for back-to-school checkups over the summer.
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Routine childhood vaccinations -- jabs that help stave off devastating illnesses such as polio, measles, diphtheria and pertussis -- are carefully laid out in Centers for Disease Control and Prevention guidelines, and all states require these vaccines for children attending public school.
While most kids are up to date on routine vaccines, according to Burgert, a significant number missed appointments over the summer. In August, the nonprofit group Health Efficient estimated that community health centers would need to increase the number of childhood vaccinations by 265% to match pre-pandemic levels -- and maintain that pace for at least six months.
"If kids need routine shots, either we are giving them at the same time, or we are prioritizing the COVID shot right now," Burgert added. "This is still a global emergency."
Pediatricians of children who need to get back on a regular vaccination schedule should consult the CDC schedule for vaccine catch-ups, even if that means some kids will be getting their shots slightly later than would be ideal, said Dr. Alok Patel, a pediatric hospitalist at Stanford Children's Health.
"I also have parents that prefer to space them out," said Burgert, especially kids historically more reactive to the flu shot. "Parents are a little bit more hesitant to do both at the same time, just because they don't want them to feel bad. And I understand that."
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Patel said he hears similar concerns: "A lot of parents say, 'Hey, this is too many shots for my child to handle.'" But spacing out the vaccines, Patel added, is not without risk.
"The problem with spacing out the vaccines is you leave your child at risk to get the diseases while you're spacing them out," said Fisher, the pediatric infectious disease expert. "There's no advantage. There's no evidence that giving them at the same time increases the adverse events. And the disadvantage is you leave your child susceptible."
According to Patel, parents should focus most on "getting their children the right protection, and getting them fully vaccinated against COVID-19 as soon as possible, but also making sure that they're getting complete protection against the other major vaccine-preventable illnesses."
Pediatricians are urging eligible patients to seek out COVID-19 vaccines as soon as possible -- and to stay up to date on other routine vaccines.
"The last thing we want to do," Patel told ABC News, "is see a resurgence of these preventable diseases because of lapses in coverage."
"These kids have been living all of this stress with us," Burgert said. "They have been living through it, and they want it to be over too. They want it to be over for their friends, and they want it to be over for their parents."
Lauren Joseph, a student at Stanford Medical School, is a contributor to the ABC News Medical Unit. Dr. Tushar Garg and Dr. Jay Bhatt contributed to this report.