Nigeria's president-elect says he will rid his nation of terrorism. But 33,000 displaced Nigerians at the Minawao refugee camp in neighboring Cameroon do not foresee an imminent homecoming.

Mohamadou Ousman hums the Nigerian national anthem as he draws water from a deep well at the Minawao refugee camp. He has been in good spirits since former military general Muhammadu Buhari won the Nigerian election two weeks ago.

During the campaign, Mr. Buhari repeatedly promised that he would root out Boko Haram. On Tuesday, he repeated this promise, writing in an op-ed column in The New York Times that he would prevent the Islamist militants from terrorizing Nigeria and its neighbors.

“What I can pledge, with absolute certainty, is that from the first day of my administration, Boko Haram will know the strength of our collective will and commitment to rid this nation of terror, and bring back peace and normalcy to all the affected areas,” he wrote.

Recommended: Think you know Africa? Take our geography quiz. At the United Nations-run Minawao camp in Cameroon’s Far North region – 75 miles from the Nigerian border – most of the 33,000 Nigerian refugees were unlikely to read his column. But many did hear his televised election victory speech in which he said he'd “spare no effort” in fighting against Boko Haram.

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“It’s reassuring to know that the president is committed to wiping out these criminals. Buhari is a soldier and I sure know he will do the job,” says Mr. Ousman. In 2013, he fled to his hometown of Bama in Borno State – often considered the base of the insurgency—for Cameroon.

But even with Buhari’s military background, coupled with recent bullish announcements by the Nigerian military, Ousman is not certain he wants to return. The trauma is still real for him.

“Even if I went back, I wouldn’t know where to start,” he says. “They killed all my brothers and sisters: thirteen of them. They slaughtered my father when he told them he would not join their campaign of murder.”

Upper hand over insurgents? In February, more than 74,000 Nigerians crossed into the Far North region of Cameroon, including 25,000 who escaped clashes between regional military forces and Boko Haram, according to the UN refugee agency.

During the election campaign, multinational troops stepped up their fight against Boko Haram; Nigeria’s army chief of staff claimed that the military had retaken all but three towns formerly held by militants.

Still, it's unclear to what extent the military has the upper hand after years of setbacks. In his op-ed, Buhari admitted that it was unlikely that he could return the 200 schoolgirls from Chibok who were kidnapped by Boko Haram a year ago.

And for Elizabeth Andraus, another camp resident, it is not enough to convince her that she should return. Rumors of liberated towns swirl constantly around the camp, but few trust the military who often give them false information. “It seems better to stay here and live on the good will of others than go back to live with the trauma,” she says.

Cameroon at capacity The Minawao camp was not built for 33,000 residents; it's designed to provide basic relief like blankets and soap, and services are in short supply.

According to the UNHCR, there are currently only 400 toilets in the camp, meaning one toilet serves 82 people instead of the recommended 50 people. Water shortages are common and the Cameroon Fire Brigade has to truck water to the camp.

During a recent visit, UNHCR head António Guterres said the relief efforts were inadequate. His agency launched an appeal last week asking for $174.4 million to help some 192,000 refugees fleeing Nigeria into Chad, Niger and Cameroon.

In the appeal, UNHCR said aid agencies in the region were struggling to provide sufficient shelter, food, clean water and sanitation to refugees.

Cameroon is also struggling to accommodate another 244,000 refugees along their eastern border with the Central African Republic.

The twin refugee crises, coupled with the war against terrorism, are straining the Cameroon’s economy to breaking point, says René Emmanuel Sadi, the minister of territorial administration and decentralization.

He adds that Cameroon will continue to show hospitality to people in distress, but also insisted that “those who wish to go back to their countries should do so, especially with the green shoots of peace already showing up in the Central Africa Republic.”

Even with the conditions at the camp, Ms. Andraus has few complaints. She is happy to have escaped her hometown of Dikwa in Borno state. She even named her three-month-old baby, born in the camp, Cameroon, as a tribute to the country that has given her family refuge.

“I lost everything, but I was lucky to have escaped to Cameroon along with my husband and kids.”