A distraught mother is trying to learn the name of a doctor who allegedly molested her 17-year-old daughter at NewYork-Presbyterian Hospital while she waited just outside her room. The teen was admitted to the Children’s Hospital in upper Manhattan on Nov. 17 and assigned a room on the fourth floor, according to a lawsuit filed by her mother. Her mom kept a bedside vigil until a young, white, male doctor came to the room on Nov. 19 at 4 p.m. and asked her to wait outside, the family’s attorney, Yair Bruck, told The Post. The doctor left after 20 minutes without saying a word, the suit says. “My daughter appeared upset,” the mom recalled in court papers. She was shocked to learn that the doc had “forcefully touched [the girl’s] vagina and breasts and exposed his penis to her while touching himself and [her],” the suit says. “During this time, the doctor advised my daughter of his desires to have intercourse with her,” the mom says in court papers. She’s suing the hospital to learn the doctor’s identity. A hospital spokeswoman declined to comment.