The teenager's mother and father, who cannot be named for legal reasons, are on trial accused of luring her to Bangladesh to execute the plan.
In a pre-recorded interview played to jurors at Leeds Crown Court on Monday, she said she felt "almost suicidal" when her family started pressuring her into accepting the proposal.
During the interview, the teenager told a police officer her parents had said they were going on a six-week holiday to Bangladesh to visit family and celebrate Eid.
However, days after landing on July 3 2016, her father supposedly informed her he had "planned a lot of things" for her future.
She said: "He just told me that that the main reason for the holiday was not just for my mum, but it was for me to get married.
"He said, 'I have planned this for years, the guy is really suitable, I've given him money for university, and he's a really attractive guy for round here'.
"He was trying to get me to say yes, but at no point did I say yes. I thought it was disgusting because it was my first cousin and stood my ground."
The teenager said she was told she would "live like a queen" and that rejecting the proposal would "bring shame" on her family.
The alleged victim said her father told her he had the "power" to force her into the plan, and that violence would be used to coerce her.
Discussing the "constant pressuring", she said: "He told me that he had brought me up over 18 years with love, but that he would chop me up in 18 seconds if I disrespected him and didn't agree.
"As the days went by, verbal abuse turned to physical abuse and my dad hit me over the head one day. It was so bad that the whole room literally went black.
"I thought, if the worst came to the worst, then I would get married and come back to England, and file a report saying what had happened.
"But my mum said there was no way that that would happen, because they were going to leave me there for a year so that I would get pregnant so that he (the first cousin) could get a visa."
The court heard that the teenager, who was studying for her A-levels at the time, "couldn't sleep or eat" because she was so scared.
She said that, with the help of her younger sister and boyfriend, she contacted the British High Commission and was "rescued" days before the wedding was due to take place.
At the end of the interview, she said she wanted her father, who moved to England from Bangladesh when he was seven, to be "punished" and she did not want to speak to him again.
The parents, who listened to proceedings through a Bengali interpreter, are accused of forced marriage and using violence, threats or coercion to force their daughter into marriage.
The trial, expected to last three weeks, continues on Tuesday.