(CNN) Imvepi Refugee Camp, Uganda: Seventeen-year-old Blessing Akujo stands motionless, watching the flatbed trucks fill with their human cargo in the midday sun.

Hundreds of her fellow refugees pack UN-issued water canisters and mattresses into the trucks before climbing in for what they hope is the final move in their desperate search for sanctuary.

Blessing's caseworker from the World Vision aid agency finally spots her, handing over the teen's newborn baby before helping mother and child up the homemade wooden ladder and into the last truck.

The engines start, the cabs rattle and the convoy sets off for one of the few remaining clear plots of land in Northern Uganda's Imvepi Refugee Camp.

Blessing Akujo sits with her newborn daughter after fleeing her homeland of South Sudan, leaving her parents behind.

Blessing's mother and father don't yet know they are grandparents. A week ago the family's village was attacked, and their neighbors were killed. In the chaos, her parents told their heavily pregnant daughter to run, promising they would follow.

"The Dinka were slaughtering people. I saw three people killed," Blessing tells CNN. "They were slaughtered," she repeats, using her hand to motion a knife on the back of her neck.

For three days, Blessing ran and hid, ran and hid, making her way south towards Uganda with other refugees.

As she crossed the border, she collapsed and there -- in front of police and soldiers -- she gave birth.

Several informal crossings like this stretch along the border, where authorities conduct a quick weapons check before welcoming refugees to Uganda.

Uganda's open borders under pressure

Uganda now has the unenviable distinction of hosting the world's largest refugee camp, Bidi Bidi. But the settlement, with a population of 272,000 refugees, is just part of the story.

There are several settlements in northern Uganda hosting South Sudanese refugees. Imvepi, one of three camps established in December in response to the growing humanitarian crisis, is already home to close to 75,000 refugees.

All told, nearly one million South Sudanese refugees are in the country, with an average of 2,000 more streaming across the border every day.

The country's policy of giving refugees land, the right to work and the right to the same services as its citizens is as admirable as it is unique.

But the sheer scale of the crisis means the system is at a breaking point.

"If Uganda is saying it is overwhelmed, it's true," says Opiyo Denish Odoki of the International Rescue Committee.

He is one of just two physicians caring for a population of 48,000 in Bidi Bidi's Ward 2.

Opiyo Denish Odoki visits one of his patients at the Bidi Bidi settlement. "We need help for these structures to be permanent so that we give better quality service," says Odoki, "Even if they are refugees, they are human beings, they have their rights."

Unsustainable aid

International agencies are facing budget issues as well. In real terms, the World Food Programme's shortfall of $59 million over the next six months means that by June 1, the operation will begin running out of food.

Already, rations have been cut in half for the 200,000 refugees who arrived before mid-2015.

It was a famine declaration in February that kick-started an aid effort for South Sudan, but the unabating violence that keeps refugees flowing across its southern border is turning an emergency situation chronic.

New arrivals search for their registration number at Uganda's Imvepi Refugee Camp. Once on the list, they can begin the process of settling on a plot of land and within five years, the hope is that they become self-sustainable.

"They were coming, so many with injuries secondary to the fighting on that side, some of them with gunshot injuries, big knives," says Odoki.

"[Survivors] have been telling us the stories of children, brothers, sisters being killed and how they survive, you never know."

What's behind the exodus?

The world's newest nation slipped into a brutal civil war in 2013, just two years after its independence, when President Salva Kiir fired his Vice President Riek Machar, who comes from a rival ethnic group.

It is tribal, it is absolutely tribal, so on that basis, it is genocide. Priti Patel, UK international development secretary

The UN's Special Adviser on the Prevention of Genocide warns that the ongoing conflict has acted "as a smoke screen" for the "deliberate starvation, the bombardment of and attacks against civilians" on the basis of their ethnic identity.

During a visit to Uganda's refugee camps, the UK International Development Secretary Priti Patel went one step further, telling reporters, "It is tribal, it is absolutely tribal, so on that basis, it is genocide."

It's just an hour before the border point closes as an old man slowly makes his way across the makeshift wooden bridge from South Sudan.

He stops just long enough to let out a shallow cough before turning up the dirt path to Uganda.

Pastor Fabian Richard Wani tries to help a young woman whose mattress was stolen. Wani fled after his congregation was attacked. "Even church leaders, we weren't safe," he says.

An unrelenting flood

Further up at the checkpoint, Ugandan police perform their last searches of the day. Victor Patrick unties a TV that's expertly balanced on the back of his motorcycle and opens a suitcase for police to look through.

"If you stay there," says Patrick, motioning toward South Sudan, "it will be until you're killed."

He's been using his prized motorcycle to ferry goods for refugees looking to escape. It's a job he used to do with his brother.

Victor Patrick has been helping the displaced carry the few belongings they were able to escape with to their new home in Uganda.

"My brother? They shot him with a gun. Right here," he says punching his heart. "The soldiers, they don't ask -- they just shoot. If you are running, that's when they shoot you."

Patrick says every person that crosses the border carries stories of loss, targeted, he says, because of their tribe. He follows with the few possessions they are able to save.

'Born of war'

The vast majority, around 86%, of those making the journey are women and children. Just 2% are elderly.

60-year-old Jaclyn Nyoka was part of the first wave of refugees to flee Bidi Bidi, turning it into the world's largest refugee camp. "More and more are coming," she says, "They are coming."

But 60-year-old Jaclyn Nyoka was one of the first to flee. She settled in Bidi Bidi when it was still accepting new refugees. Her home looks permanent. A thatched roof and mud walls hide the original white UNHCR tarpaulin.

She says she feels safe: "The Dinka are not here, we don't hear their guns. We can sleep."

But she'll never forget why she fled. "These soldiers, when they arrest you, they slaughter you. Young boys like this," she says, pointing to some curious children, no older than five, who are watching nearby. "They slaughter them. I've seen it with my own eyes."

Blessing sits in a processing center, cradling her days-old infant hoping that one day she will be reunited with her parents. As a young mother with a baby daughter Blessing will receive special protection and services.

Here, even the youngest of lives are marked by conflict.

Blessing puts her mattress on the ground outside her new home and begins feeding the daughter she has named Jerisa Sakila. Its meaning? "War," Blessing tells us, "That she was born of war."