“I paint because I need to.” The revelation of this new documentary about Frida Kahlo (yes, another one) is the white-hot brilliance of her writing. On the voiceover, Kahlo tells her story in her own words, stitched together from letters, diaries and interviews (brought to life by Mexican stage actor Fernanda Echevarría del Rivero). The end result has a raw, thrilling intimacy.

Kahlo was rebellious by nature. As a little girl she tugged on the priest’s cassock: “Was the virgin Mary really a virgin?” At college, on course to become a doctor, she wore men’s suits; in old photos, she looks like a beautiful boy. Then came the life-changing accident that nearly killed her. Aged 18, Kahlo was travelling on a bus that collided with a tram. “The handrail went through me like a sword through a bull,” she remembers. In a hospital bed for months – “trapped alone with my soul” – she began painting. Kahlo’s intensely autobiographical canvases appear on screen as she describes the moods and events they depict.

Controversially, director Carla Gutiérrez animates some of Kahlo’s work. So the hair on the floor in Self-Portrait with Cropped Hair (painted after separating from her husband, Diego Rivera), comes to life, fluttering down to the ground. These bits have outraged some Kahlo fans. What’s all the fuss about, I wonder. Can it really be worse than plastering her work over tea towels?

Then there’s a fascinating section where Kahlo describes stepping out of Rivera’s shadow; it’s like a manifesto. After a devastating miscarriage, she became obsessed with “starting over” and “painting things how I saw them, through no one else’s eyes”. She regretted wasting “my best years on a man”. After divorcing, Rivera begged her to marry him again, and Kahlo agreed on two conditions: a) she would pay half of everything; b) they would never have sex with each other. (The infidelities on both sides had been epic: she slept with Trotsky; he slept with her favourite sister).

Each new sentence adds more: more complexity, more woman. There’s the anguish and vulnerability of living with chronic pain; Kahlo is scorchingly sexy too (her love letters practically pulse with desire). She is savage about her enemies (watch out Surrealists) and swears like a trooper. On a visit to New York, where the monied art world is fawning over Rivera, Kahlo sticks a pin in his ego: “Diego is big shit here.”

• Frida is in UK cinemas on 8 March and on Prime Video on 14 March.