No, Howard's Mill is not a true story. It's likely a product of the author's imagination or inspired by various fictional elements. True stories typically have verifiable sources and documentation, which is lacking in this case.
Chester Bennington had a troubled back story. He had a difficult childhood filled with abuse. This led to his struggles with mental health issues throughout his life. His experiences of pain and trauma influenced his lyrics which were often very emotional and raw.
It depends on your perspective. Some parts of Howard's Mill are based on actual occurrences, while others might be fictionalized for dramatic effect. But there is a core of truth to the story.