Does writing about negative events in your life help your brain?

Maybe. Here’s a 2019 article which suggests it does (and even suggests some of neurological mechanisms with reference to learning): Effects of Expressive Writing on Neural Processing During Learning.

But, as with all things psychologically related—especially trauma related—I would proceed with caution, and with a professional. We are just beginning to understand the neurological relationship between emotions, memory and cognition, and the brain isn’t a Mac which one can self-hack.