The 16-year-old, who was also allegedly targeted, gets panic attacks and often wakes up in the middle of the night. She even tries to run from her ward, the doctors say.
Over two years, her mother was gang-raped several times, allegedly by a group including Mr Prajapati. Eight months ago, the attackers allegedly turned on the teen. Mr Prajapati is among the accused named in a police complaint, which is an embarrassment for the Akhilesh Yadav government in the middle of state polls.
"They tried to rape me and held my mother tight as she kept crying and pleaded with them to stop. They threatened her before setting me free," the girl said on Wednesday, speaking between long pauses.
"I want to see Prajapati and his men who attempted to rape me behind the bars. He has ruined our lives permanently. We had to leave our hearth and home to save our lives," the Press Trust of India quoted her as saying.
Policemen from Uttar Pradesh have visited the hospital twice to speak to her but were denied permission.
Her mother, who alleges she was exploited on the promise of a position in the ruling Samajwadi Party and sand mining contracts, moved the Supreme Court after her complaints to the police were allegedly ignored. On the court's order, an FIR or complaint was filed against the minister on February 18.
"Constant threat calls from Prajapati's men warning us not to pursue the matter became unbearable and we decided to leave UP to save our lives. My mother then approached the court," said the teen.
On Tuesday, a police team searched Mr Prajapati's homes in Lucknow and other cities and said he could not be found.
The 49-year-old minister is a candidate in the Uttar Pradesh election and was last seen campaigning in Amethi, where he is contesting. His request for protection from arrest will be heard by the Supreme Court on Monday.
The girl is haunted by what happened to her and her mother.
"I couldn't take the exams this year....our lives were a mess," she said, hoping she can sit for her Class 10 examinations next year.
Doctors at AIIMS say she is "living in constant fear. She is unable to sleep. We have put her on medication and she is undergoing behavioural therapy."
With inputs from PTI