Just a kilometre from the Jordanian border, Om Suleiman and her children are sleeping in a small shed they share with five other Syrian families. About 20 people are crowded into this hot, insect-ridden space, and Suleiman worries about the scorpions that come at night.

Just days ago, she and her children rushed from their home in Tareeq al-Sad, a rebel-held neighbourhood in Deraa. “We escaped at night, terrified and barefooted,” she says.

Her family are among a wave of Syrian civilians who have fled their homes in southern Syria over the past few weeks after a relentless aerial bombardment by forces loyal to the country’s president, Bashar al-Assad. Suleiman knew it was time to leave when she heard the all too familiar din of improvised munitions, known as “elephant rockets” because of the thunderous sound they make. The weapons are among many witnesses say are being used against civilian neighbourhoods in south-west Syria.

Deraa was meant to be shielded from the fighting as part of a “de-escalation agreement” brokered last July by Jordan, the US and Russia. But the truce started to unravel last month when a government offensive began targeting the opposition-held part of the province.

Shelling and air raids are believed to have killed more than 200 civilians. The UK-based Syrian Observatory for Human Rights has said at least 30 women and 26 children are among the casualties.

As the Syrian regime and its ally Russia continue to pound the rebel enclave, Deraa residents must decide whether to flee or hunker down in their homes. “The situation is beyond comprehension,” says Israa al-Rifai, a local activist who recently escaped with her family to the opposition-held city of Nasib. “People were confused whether to keep their eyes on the sky to watch the warplanes or to get in the car and leave.”

Rifai describes watching panicked families piling into trucks at all hours of the day and night. “Women were crying, and children were laughing in the trucks because they didn’t understand what was happening,” she says.

For the Assad regime, recapturing this portion of Syria, which borders Israel and Jordan, would mark a strategic and symbolic victory. Deraa is considered the “cradle of the revolution”, and was the epicentre of the 2011 anti-government protests that set in motion Syria’s seven-year war.

Since 19 June, the fighting has sent thousands of people into opposition-run areas of south Deraa and Quneitra,according to UN estimates. Jordan, which already hosts an estimated 1.3 million Syrian refugees, said it could not absorb any people now stranded near its northern border.

Refugees flee Deraa with their belongings. Photograph: Alaa Al-Faqir/Reuters

The hashtag #OpenTheBorders has started trending on Twitter.

Displaced families have found refuge in schools and government buildings, according to Mousa al-Zoubi, who heads the Deraa provincial council’s newly formed emergency committee. But the majority, he says, are sleeping in the streets and in olive groves: “Their mattresses are the ground and their blankets are in the sky.”

The lucky ones are able to buy tents, which street vendors are reportedly selling for as much as $250 (£189) each. Others, like Rifai, brought tents with them. “I had never imagined that one day I would be living in a tent,” she says. “It’s so difficult for me to adapt, but at least I am away from the bombing.”

The escalation in fighting has cut off major supply routes, which has led to price hikes on items such as diesel and processed food. The World Food Programme has delivered supplies to more than 180,000 people through the Ar Ramtha crossing between Jordan and Syria, which spokesperson Marwa Awad says is “the only lifeline now”.

The UN, which estimate that 750,000 civilians are at risk in south-west Syria, has warned Deraa could become a repeat of the humanitarian disaster seen in eastern Ghouta earlier this year.

Zoubi is calling on the international community to do more to prevent that from happening. “All we’ve heard from international organisations are just promises,” he says. “We are relying on individual donations to secure the essentials.”

Syria’s rebels also feel abandoned. Last month, Reuters reported that the US government told the heads of the Free Syrian Army not to expect any support. Ibrahim al-Jebawi, a former FSA official and current spokesperson for an opposition-linked media group in southern Syria, said he wasn’t surprised. “We’ve never counted on America to intervene. That’s been clear since the first chemical attack on Ghouta in 2013,” he says.

He adds that the rebels “will fight until the end, regardless of the US attitude”.

Alaa al-Dweri, who repairs motorcycles, described a doomsday scenario playing out in his town of Busra al-Harir, as livestock roamed the streets and families drove to safety in packed cars.

Dweri, who doesn’t own a car, managed to get his wife, three children and a few small bags on his motorbike. The family of five headed for Tal Shihab,near Quneitra province, and are staying at a home belonging to friends.

“I wish I could have helped other families to escape, but unfortunately I only have this motorbike,” he says.