Hussein Khamis was shot in the leg during the attack.
"After I was injured, there was no-one to carry me," he said.
Mr Khamis managed to reach a nearby hospital despite his injury, but he "found no-one, everyone had fled".
Eventually he managed to get a lift to Tawila. Like Ms Mohammed, he says he was robbed along the way.
The RSF has not commented on these specific allegations.
MSF said that it had received more than 170 people with gunshot and blast injuries in Tawila since the attack, 40% of whom have been women and girls.
"People tell us that many injured and vulnerable people could not make the trip to Tawila and were left behind. Almost everyone we talk to said they lost at least one family member during the attack," said Marion Ramstein, MSF's project coordinator in Tawila.
Zamzam was established in 2004 to house internally displaced people fleeing ethnic violence in Darfur.
Its seizure would be strategically significant for the RSF, which last month lost control of Sudan's capital, Khartoum.
The RSF remains in control of much of western Sudan, including most of Darfur.
This week the group announced plans to launch a parallel government in the parts of Sudan in controls, heightening fears Sudan could ultimately split in two.
Safe, at least for now, Ms Mohammed reflected on the immense loss this war has caused those like her.
"We want the war to stop," she said. "Peace is the most important thing."