“So many days are filled with this puzzle of: We don’t have enough beds for this patient who wants to come, so how are we going to shuffle our children around to accommodate one more?” said Devon H. Relle, a pediatric nurse practitioner at Children’s Hospital New Orleans, where she worked the front desk of the 17-bed I.C.U. The hospital was also seeing an early, worrisome wave of respiratory syncytial virus, known as R.S.V., which can cause some of the same symptoms and was contributing to the overflow conditions.

The crush of Covid-19 at Children’s Hospital grew so intense this month that the state called in a federal “surge team” of emergency responders from the Department of Health and Human Services’s National Disaster Medical System. The group of about 14 included a physician, a nurse practitioner, nurses, paramedics, a respiratory therapist and a pharmacist…

“I’ve had to kind of make peace with that people are not doing what they’re supposed to. The kids are suffering,” Mr. Melancon said. “Not that I accept it, but if I get hung up in the anger of it, I would walk around confronting people in Walmart, here, everywhere.”

“I can’t tell them, ‘Why didn’t you isolate this kid?’” Mr. Melancon continued. “So we just tell them, ‘Your kid has Covid. It’s really hard on the lungs. Your child’s very sick. We’ll do everything we can to get him better.’”