In excruciating pain with lesions on her face and scalp, Tracey Fine lay for 13 hours on a gurney in an emergency room hallway.

All around her, Covid-19 patients filled the beds of the hospital in Madison, Wis. Her nurse was so harried that she could not remember Ms. Fine’s condition, and the staff was slow to bring her pain medicine or food.

In a small rural hospital in Missouri, Shain Zundel’s severe headache turned out to be a brain abscess. His condition would typically have required an operation within a few hours, but he was forced to wait a day while doctors struggled to find a neurosurgeon and a bed — finally at a hospital 375 miles away in Iowa.

From New Mexico to Minnesota to Florida, hospitals are teeming with record numbers of Covid patients. Staff members at smaller hospitals have had to beg larger medical centers repeatedly to take one more, just one more patient, but many of the bigger hospitals have sharply limited the transfers they will accept, their own halls and wards overflowing.