The nine-year-old was admitted to Altnagelvin Hospital in Londonderry in June 2001, before being transferred to the Royal Hospital for Sick Children in Belfast, where she died 36 hours later.
On Friday, Banbridge Courthouse heard Raychel's nursing care described as a shambles, and the note-taking labelled a disgrace.
The Ferguson family were in court, where they heard some details of the schoolgirl's death for the first time.
Raychel's death followed an operation to remove her appendix and experts said there was a lack of communication, her medical notes were inadequate and a complete disgrace.
No doctor saw Raychel more than once, and she was never seen by a senior consultant. The inquiry heard blood tests which may have prevented the nine-year-old's death were never carried out.
"It was outrageous. A simple blood test that day could've saved Raychel's life and that was not taken," said her mother, Marie Ferguson.
"I want the truth," she told UTV.
"I want what happened to Raychel out there in the public, because I know it's too late for Raychel but hopefully it will save other children's lives."
The deaths of four-year-old Adam Strain at the Royal in 1995 and of nine-year-old Claire Roberts there a year later are also being examined by the public inquiry.
In addition, the investigation is looking into events following the 2000 death of 17-month-old Lucy Crawford, and specific issues arising from the treatment of 15-year-old Conor Mitchell in the Royal.
The inquiry will not sit on Monday, which would have been Raychel's 21st birthday, and will resume on Tuesday.