At one point, she says, "there was no-one to turn to in the school and I felt so low I didn't want to go on".
According to research for BBC School Report, half of teenagers with mental wellbeing issues try to cope alone.
And a third said they were not confident enough to speak to a teacher.
At her lowest point, Grace made a "suicide video", which she posted on YouTube.
"I'd get beaten up every week," she says.
"Teachers wouldn't do anything. I even heard the teachers talking about me behind my back."
According to her mother, Sarah, Grace got some help through external music therapy and counselling but little support directly from her first two schools.
Support is better at her third school, where she helps as an anti-bullying ambassador.
She is also a member of the National Anti-Bullying Youthboard.
ComRes researchers questioned a representative sample of more than 1,000 UK-based 11- to 16-year-olds for BBC School Report:
They said the most important thing schools could do to support pupils' mental wellbeing was to provide someone trustworthy to talk to confidentially, but:
Separate research on just over 700 teachers found:
In January, Prime Minister Theresa May announced plans to transform attitudes to mental health, with a focus on children and young people.
The plans include better links between schools and NHS specialist staff and mental health first aid training for every secondary school.
Reacting to the School Report research, Edward Timpson, Minister for Vulnerable Children and Families, said the government would "transform mental health services in schools" and was commissioning research to help schools identify which approaches worked best.
"Growing up in today's world can be a challenge for children and young people, so it's vital that they get the help and support they need," said Mr Timpson.
Last year, research for the children's commissioner for England suggested more than a quarter of children referred for mental health support received no treatment.
And on Thursday, commissioner Anne Longfield said the School Report study highlighted "many desperately sad stories" of children with serious conditions being denied support.
She called for urgent action from schools, the NHS and government.
The Family Links and Nurturing Schools Network said schools needed better staff training and enough resources to support and improve pupils' emotional and mental health.
"We must go further to invest in preventative approaches in schools and at home," said the network's chief executive, Nick Haisman-Smith.

Northern Ireland international Little has scored two goals in 16 games for Preston since signing from Scottish side Rangers in June 2014.
The 26-year-old made five appearances on loan at Blackpool earlier this term.
Fosu, 20, has played once for Reading, but featured in six games for Fleetwood after joining on loan in November.
"Andy's suffered with injuries this year so this is a chance for him to get some football and get himself back on track," Stanley manager John Coleman told the club website.
"When you've not played for while you just want to play and I think the exposure to the first team he'll get will do him good."
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The 55-year-old's death is being treated as 'unexplained' by police.
Police say they want to trace a woman who may have more information about how the victim came to sustain his head injuries.
They also asked for people in the Prince of Wales Avenue and Oxford Road area between 02:00 and 02:30 BST on Sunday to come forward.
The woman sought by police is described as mixed-race, 5ft 2ins (1.57m) tall, aged around 35, and slim with long wavy black hair.
Grace, 16, has been bullied for the past nine years, has moved schools twice, struggled with suicidal thoughts and taken medication for anxiety and depression.
[NEXT_CONCEPT]
Promotion-chasing Accrington Stanley have signed Preston striker Andy Little and Reading winger Tarique Fosu on loan until the end of the season.
[NEXT_CONCEPT]
A man has died in hospital after being found unconscious inside a property in Reading in the early hours of Sunday.