A migrant mother is blaming American border authorities for her 5-month-old daughter's contracting pneumonia, saying that she and her child were kept in a "freezing" holding cell while in U.S. custody.

The infant is now hospitalized in North Carolina, said the 23-year-old mother, who is from Honduras and asked to identified by only her first initial and last name, A. Portillo, because she is fleeing an abusive partner.

The baby was on Thursday morning in good condition, according to Southeastern Regional Medical Center in Lumberton, North Carolina.

U.S. Customs and Border Patrol agents detained her and her daughter on Dec. 12, after they crossed the border illegally by going over a fence, Portillo said.

A 5-month-old migrant baby receives treatment for pneumonia at Southeastern Regional Medical Center in Lumberton, N.C.

She said that because of harsh conditions while traveling up from Honduras through Mexico, her daughter became ill.

When they stopped in Mexico City, the infant received medical care and the mother was given an antibiotic to take with them.

"She recovered completely" in Mexico City, Portillo told NBC News. Once they reached the border city of Tijuana, the baby was still "perfectly healthy."

In Tijuana, the mother and child stayed in a shelter that flooded during a massive rainstorm and had to evacuate, she said.

"That's when I decided to cross into the United States, to seek help," the mother said.

She told NBC News that border agents took the antibiotic from her. “If I had been able to keep the drugs, maybe they would have made my baby better.”

Portillo said that she and her child were kept inside "freezing" holding cells for two days in San Ysidro, California. They were then taken to San Diego where they were held in custody for three more days.

Migrants often call the holding cells “hieleras,” or iceboxes, because of their allegedly low temperatures. A Human Rights Watch report from February found that detainees were often kept in cold cells for days without basic hygiene products, such as hand soap or toothpaste.

U.S. Customs and Border Patrol told NBC News on Wednesday that it is working to get more information on this case. The agency emailed an internal report dated June 2018 that says holding cells are kept clean and at moderate temperatures between 66 and 80 degrees Fahrenheit.

In San Ysidro, Portillo said she asked for medical care for her daughter. "They told me that ‘no one told me to cross the United States and that I was an invader.’"

She said she asked for medical attention for her baby again in San Diego. After passing an interview as part of her application for U.S. asylum, she and her daughter were dropped off at a church in San Diego that is operating as a migrant shelter. From there, they flew to stay with family in North Carolina.

"By the time I arrived in North Carolina, my daughter had a fever," she said. At one point the child stopped breathing, she said.

The mother said she immediately took her baby daughter to the hospital, and that doctors told her to prepare for the possibility that her daughter may die.

Portillo and her daughter were part of a migrant caravan of roughly six thousand men, women and children, mostly from Central America, who traveled to the U.S. to seek asylum or legal residency. The caravan arrived in Tijuana, Mexico, in mid-November.