Tijuana, Mexico (CNN) Tents cover most of the dirt on the baseball diamond. Pants are hanging out to dry on top of the bleachers. And the scoreboard at Little Padres Park is blank.

There's no room for sporting events here now.

This municipal sports complex in the Mexican border city of Tijuana is packed with people . But it's been transformed from an athletic facility into something entirely different: a temporary home base for thousands of Central American migrants who say they have nowhere else to go.

A man steps across mud after taking a shower at the shelter.

A man steps across mud after taking a shower at the shelter.

People line up for food at the shelter. Members of the Mexican navy have set up mobile kitchens where they prepare and distribute meals. But the wait can take hours.

People line up for food at the shelter. Members of the Mexican navy have set up mobile kitchens where they prepare and distribute meals. But the wait can take hours.

Luis Rene Reyes Garcia, a 28-year-old from Guatemala, reads a donated Bible as he rests on the street outside of the shelter.

Luis Rene Reyes Garcia, a 28-year-old from Guatemala, reads a donated Bible as he rests on the street outside of the shelter.

Many staying in the shelter are sleeping outdoors -- some in tents, some lying on the dirt in sleeping bags or blankets.

Many staying in the shelter are sleeping outdoors -- some in tents, some lying on the dirt in sleeping bags or blankets.

Well-wishers hand out donated clothes from the trunk of a car outside the shelter.

Well-wishers hand out donated clothes from the trunk of a car outside the shelter.

Miguel Angel Luna gets his hair rinsed as he undergoes a treatment for lice on Monday, November 26. A group of local volunteer nurses had set up outside the shelter to help.

Miguel Angel Luna gets his hair rinsed as he undergoes a treatment for lice on Monday, November 26. A group of local volunteer nurses had set up outside the shelter to help.

A woman tries to sweep away floodwaters between bouts of heavy rain on Thursday, November 29.

A woman tries to sweep away floodwaters between bouts of heavy rain on Thursday, November 29.

Migrants wait in line to receive donated items from a church group outside the shelter.

Migrants wait in line to receive donated items from a church group outside the shelter.

Clotheslines hang over tents and sleeping bags inside the shelter on Wednesday, November 28.

Clotheslines hang over tents and sleeping bags inside the shelter on Wednesday, November 28.

An aerial view of the shelter, as seen on Tuesday, November 27.

An aerial view of the shelter, as seen on Tuesday, November 27.

A migrant rests in his tent at the Benito Juarez Sports Complex, which is now a makeshift shelter in Tijuana, Mexico.

A migrant rests in his tent at the Benito Juarez Sports Complex, which is now a makeshift shelter in Tijuana, Mexico.

Many say they want to seek asylum in the United States. But the waiting list at the nearby port of entry grows longer every day. It could be weeks -- or even months -- before they have a chance to cross the border and make their case.

US officials say limited resources and capacity mean they can only process a fraction of cases on the waiting list daily.

Migrants say life is difficult here -- but the situations they're fleeing were far worse.

The Benito Juarez Sports Complex has become Tijuana's main migrant shelter. Here's what it looks and sounds like inside:

Open sewage and puddles of runoff

From the fields outside at the sports complex, it's common to see -- and hear -- helicopters flying through the air. On the other side of the border, US authorities are keeping watch.

Migrants can see the US border from here, too. The large, metal fence looms in the distance, behind the row of blue portable toilets. Nearby, not far from growing piles of trash, some use outdoor showers. Others clean themselves using bottles of water.

Runoff from showers and portable toilets leaves a nearby field muddy at the Benito Juarez Sports Complex in Tijuana, Mexico, where thousands of migrants have taken shelter as they wait to seek asylum in the United States.

Some migrants tiptoe through the mud, trying to avoid the runoff from the nearby bathing and bathroom facilities. Children play in the puddles.

At times, the stench of sewage fills the air.

Sudden shouts for help

The shouts came suddenly on Wednesday afternoon.

"Careful! Careful! Make way!"

Three people raced into a makeshift medical clinic at the shelter, carrying a man into an examination room and pulling a curtain behind them.

In another room nearby, Carlos Betanzos told CNN conditions inside the shelter are increasingly concerning.

"This shelter is not very clean inside. The bathrooms are very bad. They are sleeping on the floor. The sanitation is not very good," said Betanzos, who's working at the shelter as part of a medical mission of doctors and nurses from the Church of the Nazarene.

Carlos Betanzos of the Church of the Nazarene says conditions inside the makeshift shelter in Tijuana are concerning. "The sanitation is not very good," he said.

Betanzos said more than 100 patients come to their clinic daily. And more than 200 more go to another clinic inside run by the Mexican government.

Many patients show symptoms of the flu, he said. Others have lice or stomach illnesses -- all treatable.

But in such crowded and cramped conditions, he said, doctors are concerned about how quickly more serious illnesses could spread.

"We are worried" he said, "about a very big infection."

Amnesty International said this week that the shelter doesn't have enough resources for migrants housed there.

"Mexican federal, state and municipal officials separately confirmed to Amnesty International that the temporary shelter did not have sufficient food, water and health services, and that respiratory illnesses were spreading among those staying there," Amnesty said.

Clotheslines crisscrossing through the air

More than 5,800 migrants have taken shelter in the complex, according to Mexico's Social Development Secretariat. That's at least three times above the facility's capacity , said Rodolfo Olimpo, a representative from Baja California state's Special Committee on Migration Issues.

And more migrants are expected to arrive in the coming days.

City officials who run the shelter say they're doing their best but need help.

Tijuana Mayor Juan Manuel Gastelum has called the situation a crisis that he says municipal authorities can't handle on their own. Mexican federal officials, he said, must step in.

"The federal government should do its job. And that is, give us shelter, give them food, water, medicine, everything that a person needs to be dignified and have a place where they can stay dignified," Gastelum told CNN this week. "So, I need the federal government to take over this situation, and if the federal government is not capable of doing it, well, go to the ... United Nations organization that was established to help out. It's called humanitarian assistance. We need that."

Manuel Figueroa, who heads the city's social services department, said Wednesday that federal support remains minimal. While Mexico's navy is making and distributing food, he said, funding for supplies comes from the state and the city -- as does the gas, electricity and water at the facility.

A man naps at the Benito Juarez Sports Complex.

"Day by day we make the greatest effort to attend to this, without having any obligation to. ... This migratory situation is the responsibility of the federal government."

Authorities in Tijuana said Thursday that they plan to open another shelter for migrants that will house at least 3,000 people in the eastern part of the city. It could open Thursday or Friday.

In the meantime, there are hundreds of children among the thousands of migrants taking shelter at the sports complex. A playground inside provides some relief from the squalor.

But days after tensions flared and US officials fired tear gas at the border , the mood inside the large Tijuana shelter at times is somber. Some migrants say they're shaken by what happened and unsure of what to do next.

Many staying in the shelter are sleeping outdoors -- some in tents, some lying on the dirt in sleeping bags or blankets.

As the threat of rain loomed Wednesday, migrants scrambled to cover their tents with black plastic tarps.

In some of the shelter's indoor spaces, blankets have become makeshift partitions to provide privacy. Hanging clotheslines crisscross through the air.

A migrant drinks water as he waits in the shelter, where more than 5,000 migrants are living.

A woman from Honduras named Naira sat on the ground in what looked like a sea of blankets. Things haven't been going well, she said. She and her young daughter are making do, but she's realized she needs to find a way to get money so they can buy more to eat.

"There is some," she said, "but very little."

Long lines for food

Members of the Mexican navy have set up mobile kitchens where they prepare and distribute meals.

Members of the Mexican navy have set up mobile kitchens to feed migrants.

But the lines for food are long. Migrants said the wait can last for hours.

Cesar Nuñez told CNN on Tuesday evening that it had been a day since he'd eaten. He said he didn't want to take food from the mouths of women and children, who need it more.

Nuñez, 30, said he was threatened in Honduras after witnessing a crime and reporting it.

Cesar Nuñez says he was threatened after witnessing and reporting a crime in Honduras. He hopes to seek asylum in the United States.

He pointed to a scar on his leg that's a permanent reminder of violence he's determined to leave behind. Gang members attacked him with a machete, he said. Compared to that, he said, conditions in the shelter aren't bad at all.

"We have come fleeing from worse things," he said.