Arlene, who was 15 and from Castlederg in County Tyrone, went missing after a night out in County Donegal in 1994.
The main suspect in her disappearance, Robert Howard, died in prison last year.
Kathleen Arkinson said she she felt police had missed opportunities to question some witnesses.
She complained to the Police Ombudsman in 2006 about the police investigation, the inquest heard.
She said police searched her house, breaking her door down with a sledgehammer, dug in her garden, and arrested her partner, adding "insult to injury already caused by the lack of investigation".
Ms Arkinson also felt Howard's trial in 2005 for Arlene's murder was mishandled because the jury was unaware of his many convictions.
She added that after Arlene went missing, false rumours grew worse.
"The rumours were that I killed Arlene," she said.
"The whole world was talking about it."
Later, Ms Arkinson was questioned by counsel for the Police Service of Northern Ireland, who asked if it was the service's "duty to investigate every opportunity to find out what happened".
"It should have been," she replied, "but they didn't do it."
Ms Arkinson also said she became more protective of Arlene after an incident when Arlene was abused by a man in 1993.
The man was jailed for that assault.
Their mother had died three years earlier.
Ms Arkinson told the inquest of the last time she saw Arlene when she left for a disco in Bundoran, and how she had given her an money to buy chips on the way home.
She never saw her sister again.
She described confronting Howard and a family, the Quinns, who she believed had taken Arlene to Bundoran, and that she had become convinced they were telling lies over her disappearance.
Earlier, the mother of one of Arlene's friends told the inquest she became scared of Robert Howard after he told her he had killed a six-year-old girl.
Bernadette Timoney, giving evidence via videolink, said in the years before Arlene went missing she thought Howard was "an evil-looking man with drink in him".
"I didn't like the look of him," she later said.
"I didn't want to be in his company - he was very scary."
She added that she had daughters of her own and wanted to protect them.
She also said that two months before she went missing, Arlene had told her she wanted Â£200 to go to England for an abortion and insisted her family should not know.
She said Arlene became hysterical when she asked her if she had gone to get the money from a bank machine with Howard, or if Howard had done anything to her.
Ms Timoney said she had not told social services or the police about the incident because she did not want to get involved.
A sister of Arlene Arkinson has told the inquest into her death police did not treat her disappearance with the "seriousness and credence" it deserved.