Below the shattered windows of the high-rise hotels in downtown Acapulco, people walk alongside towering hills of garbage bags filled with rotting food and debris, from mattresses to Christmas decorations. Volunteer firefighters from distant states clear the waste, wiping away swarms of cockroaches from their arms.

Miles from the coastal beachside resorts, Elizabeth Del Valle, 43, listened as her teenage daughter Constanza Sotelo, described the “mountains of trash” still blocking many streets surrounding their home.

“We have no way to find face masks to keep ourselves healthy,” said Ms. Del Valle. “We expect that we’re going to get an infection from the smell, from the garbage.”

Weeks after Hurricane Otis shocked forecasters and government officials by intensifying rapidly into the strongest storm to hit Mexico’s Pacific Coast and devastate much of Acapulco, residents say they now face an unfolding public health disaster.

Many locals, public health officials and emergency responders say they believe that the uncollected garbage is linked to stomach infections, diarrhea and skin rashes and other ailments that people have complained about since the storm.

Local business groups this past week called on federal and state officials to declare a sanitary emergency citing “the accumulation of garbage, construction material, lack of potable water and the presence of insects and harmful fauna,” including human remains.