Sophie, from Whitstable, detailed her struggles for a BBC animated film as part of Mental Health Awareness week.
She is still on a waiting list for specialist support from the Kent and Medway NHS trust months later.
The chief executive has written to Sophie offering her "personal and unreserved apology".
In 2016, Sophie - who was diagnosed with borderline personality disorder - tried to kill herself three times in one week and was admitted to hospital each time.
She was discharged shortly afterwards with no support.
Sophie, who is in her early 20s, said the first thing the consultant said to her was: "We're discharging you."
She was told it would be six months before she got any help.
"I've totally given up. It doesn't feel like I'm every going to get any treatment," Sophie said.
In a letter to Sophie, trust chief executive Helen Greatorex said: "It is not right or fair that people in distress (as you were) feel unsupported by mental health services.
"My letter to you Sophie, therefore has two purposes," she wrote.
"The first is to offer you my personal and unreserved apology that your experience of services was not what we would want for anyone.
"The second is to say that we completely agree that things need to change, and as you can see, we are working on those changes now."
Ms Greatorex said the trust was working to develop a new strategy to help people such as Sophie and has invited her to talk to senior managers to help shape changes to the service.
A woman who was discharged from hospital shortly after trying to kill herself three times in one week has been offered an apology from the trust.