People also drink from hafirs (natural reservoirs) and we see a worrying number with diarrhoea.
From the border to Jamam is about 50 to 60km, a very long way when travelling on foot and without water. At Kilometre 43 - the informal transit point - water quickly ran out.
The population was forced to walk to Kilometre 18 (K18) in search of more and Medecins Sans Frontieres set up water stations and oral rehydration points along the road.
But, tragically, every day our teams saw people with acute dehydration as they walked and some died despite attempts to revive them. They were simply too weak to survive.
At K18, again there wasn't enough water for more than a few weeks. It was clear the refugees had to keep moving so UNHCR and other agencies agreed to set up a new camp in Batil, and some of this K18 population has started to be moved there. This is not an easy journey because of the rain and the roads but, bit by bit, as the weather allowed, the people have been moved in buses and trucks.
We've tried to be supportive in addressing diarrhoea, respiratory infections and severe malnutrition. In the past week we've seen an increase in malaria, too, and a very significant number of eye infections across the whole population. This is a sign people are struggling to manage their hygiene; they simply don't have the water to stay clean and wash clothing and blankets.
And now with the rain, hypothermia is a real risk for a malnourished child. Their small bodies are unable to regulate their body temperature, their blankets and clothes get wet and they get cold. For children already vulnerable, there is a huge illness risk and some will die.
On the move for weeks, sometimes for months, the closer this community comes to shelter, consistent food distribution and the prospect of a safe new home, the more they want to get there so it becomes chaotic as trucks are loaded and unloaded.
Serious cases came off nearly every truck: children with high fever and people severely dehydrated, malnourished, drowsy and hypoglycaemic. We've had women getting off buses already in labour, people with malaria and many in need of 24-hour hospital care.
People have to make very tough decisions. If a child is really sick, mothers have to find a way to split their care between that child and others. It's an unbearable reality.
Some families have already split up and the mother is on her own. Within this culture, it's not always easy for women to make decisions. Some evenings I've talked to women about bringing their sick child to the hospital and they say they have to wait until their husband arrives.
We're just meeting this community so we have to be patient and try to understand their needs.
During one crazy morning helping people board the buses, I encountered three women who had in their arms, buried beneath layers of colourful fabric, three very small babies, all of them underweight.
It was agreed to let the mothers and their small children return with us to Jamam hospital while the fathers and the other children went on to settle in Batil. We now have three very sweet but tiny babies here in Jamam and they're improving each day. I think if they had gone on to Batil, they might not have survived.
For acute malnutrition, a nutrient-rich paste is given to children every day but there are severely malnourished ones who have complications like malaria, diarrhoea, chest infection, or malnutrition so bad they've lost the ability to eat.
Those kids generally need hospitalisation; it's a delicate balance. It can take weeks to months to turn around a severely malnourished child. I can't say everyone is going to make it because some are simply too sick and too vulnerable. Life will remain precarious but I know there will be a lot of success stories as well.
Hopefully, in the next six weeks some of the most prevalent morbidities like diarrhoea, chest infections, skin and eye infections will start to dissipate when people get more consistent food, clean water, shelter and health care.
But the stagnant water around Jamam is a risk - already in Batil and Doro camps, teams are seeing higher levels of malaria which can be seriously detrimental to pregnant women and young children.
And there's the risk of cholera, endemic in Blue Nile State, so some of these people may already be carriers.
The geography of this place is not to be taken lightly but I think we've done a great job scaling up quickly and providing care for the most immediate health issues we can.
These people have already had a challenging journey and there are difficult months ahead for them. But they're incredibly vibrant, still smiling, saying hello and sharing their tea.
How to donate
Medecins Sans Frontieres is helping refugees in Upper Nile State, South Sudan, in three main camps: Jamam, Doro and Batil. To donate to MSF go to www.msf.org.au or phone 0508 633 324 (NZ toll-free number).
