A chaotic scene of sickness and filth is unfolding in an overcrowded border station in Clint, Tex., where hundreds of young people who have recently crossed the border are being held, according to lawyers who visited the facility this week. Some of the children have been there for nearly a month.

Children as young as 7 and 8, many of them wearing clothes caked with snot and tears, are caring for infants they’ve just met, the lawyers said. Toddlers without diapers are relieving themselves in their pants. Teenage mothers are wearing clothes stained with breast milk.

Most of the young detainees have not been able to shower or wash their clothes since they arrived at the facility, those who visited said. They have no access to toothbrushes, toothpaste or soap.

“There is a stench,” said Elora Mukherjee, director of the Immigrants’ Rights Clinic at Columbia Law School, one of the lawyers who visited the facility. “The overwhelming majority of children have not bathed since they crossed the border.”

Conditions at Customs and Border Protection facilities along the border have been an issue of increasing concern as officials warn that the recent large influx of migrant families has driven many of the facilities well past their capacities. The border station in Clint is only one of those with problems.

In May, the inspector general for the Department of Homeland Security warned of “dangerous overcrowding” among adult migrants housed at the border processing center in El Paso, with up to 900 migrants being held at a facility designed for 125. In some cases, cells designed for 35 people were holding 155 people.

“Border Patrol agents told us some of the detainees had been held in standing-room-only conditions for days or weeks,” the inspector general’s office said in its report, which noted that some detainees were observed standing on toilets in the cells “to make room and gain breathing space, thus limiting access to the toilets.”

She said the conditions in Clint were the worst she had seen in any facility in her 12-year career. “So many children are sick, they have the flu, and they’re not being properly treated,” she said. The Associated Press, which first reported on conditions at the facility earlier this week, found that it was housing three infants, all with teen mothers, along with a 1-year-old, two 2-year-olds and a 3-year-old. It said there were dozens more children under the age of 12.

Ms. Mukherjee said children were being overseen by guards for Customs and Border Protection, which declined to comment for this story. She and her colleagues observed the guards wearing full uniforms — including weapons — as well as face masks to protect themselves from the unsanitary conditions.

Together, the group of six lawyers met with 60 children in Clint this week who ranged from 5 months to 17 years old. The infants were either children of minor parents, who were also detained, or had been separated from adult family members with whom they had crossed the border. The separated children were now alone, being cared for by other young detainees.

“The children are locked in their cells and cages nearly all day long,” Ms. Mukherjee said. “A few of the kids said they had some opportunities to go outside and play, but they said they can’t bring themselves to play because they are trying to stay alive in there.”

When the lawyers arrived, federal officials said that more than 350 children were detained at the facility. The officials did not disclose the facility’s capacity but said the population had exceeded it. By the time the lawyers left on Wednesday night, border officials told them that about 200 of the children had been transferred elsewhere but did not say where they had been sent.

“That’s what’s keeping me up at night,” Ms. Mukherjee said.

Some sick children were being quarantined in the facility. The lawyers were allowed to speak to the children by phone, but their requests to meet with them in person and observe the conditions they were being held in were denied.

The children told the lawyers they were given the same meals every day — instant oats for breakfast, instant noodles for lunch, a frozen burrito for dinner, along with a few cookies and juice packets — which many said was not enough. “Nearly every child I spoke with said that they were hungry,” Ms. Mukherjee said.

At the Border Patrol’s Central Processing Center in McAllen, Tex. — often known as “Ursula” — the lawyers encountered a 17-year-old mother from Guatemala who couldn’t stand because of complications from an emergency C-section, and who was caring for a sick and dirty premature baby.

“When we encountered the baby and her mom, the baby was filthy. They wouldn’t give her any water to wash her. And I took a Kleenex and I washed around her neck black dirt,” said Hope Frye, who was leading the group, adding, “Not a little stuff — dirt.”