Multitalented artist Winnie Khumalo hopes her health will improve when she goes under the knife in J.
The National Emergency Management Agency (NEMA) said 11,442 men, women and children from Gwoza in Borno state had been registered at two facilities for displaced people in neighbouring Adamawa state.
The Islamists took over Gwoza, which lies near the border with Cameroon, on August 7 and NEMA said the town was "still under siege".
Some locals hid on a nearby mountain without food or water for more than a week, while others trekked four days to the Borno state capital, Maiduguri.
NEMA had said the insecurity had prevented teams from getting to the displaced.
But the agency's northeast information officer, Abdulkadir Ibrahim said urgent relief supplies were now being provided to 6,566 people from Gwoza in the town of Madagali and 4,876 in Mubi.
Boko Haram has in recent weeks appeared to shift tactics from hit-and-run attacks in northeast Nigeria to holding rural towns and villages, which forces residents to flee.
On Thursday, residents and a local government official said the insurgents had taken over the town of Buni Yadi, in Yobe state.
The United Nations humanitarian office (OCHA) said on August 5 that Boko Haram attacks have forced nearly 650,000 people from their homes in Borno, Yobe and Adamawa states, which have been under emergency rule since May last year.
Thousands more have fled across the border into Niger, Chad and Cameroon.
NEMA has previously warned of a humanitarian crisis in northeast Nigeria, with the influx of internally displaced people heaping pressure on nearby states for basic amenities such as food and shelter.