At a makeshift camp in Matamoros, tents crowd a muddy levee, housing around 2,500 migrants. Families cook on homemade stoves built out of old washing machines. From a trailer, Dr. Maura Sammon, the medical director for Global Response Management, leads a team of doctors, some of whom are migrants themselves.

Dr. Sammon said the team treated at least 40 patients a day. She listed the more serious medical issues: sickle cell anemia, hypoxia, third-degree burns and sepsis. Other patients included a 70-year-old with chest pains, children with epilepsy or development disorders, a migrant with H.I.V. as well as one with ovarian cancer.

“This is 100 percent a creation of M.P.P.,” Dr. Sammon said. “It is not a virtual wall — it is a wall. You see how close that river is. You see people looking at that river every day and saying, ‘The United States is right there.’”

Her team sends patients in need of emergency care to a nearby hospital, but the care can be inadequate. A boy who went to the hospital with appendicitis was discharged, then his appendix ruptured, Dr. Sammon said. Some migrants refuse to go to the hospital for fear of being kidnapped by cartel organizations, the same threat that prompted the State Department to advise Americans not to travel to Matamoros. On Thursday, a drive-by shooting near the camp forced the evacuation of Dr. Sammon’s medical team.

Homeland security officials say the new asylum policy, more commonly known as Remain in Mexico, quelled a surge of migration last year and eased overcrowded detention facilities in the United States. Forcing migrants to wait in Mexico has also discouraged those unlikely to qualify for asylum from participating in the process, officials say.

A medical issue by itself usually has not been enough to gain entry into the United States, and was rarely grounds for a claim of asylum, typically granted to those fleeing political oppression and violence. Foreigners with health conditions typically have obtained visitor visas and must prove they can sufficiently pay for medical treatment in the United States.