Is there a word for irrational anger?

There's temper, or more specifically, ill-temper.

Temper can refer to a tendency to become unreasonably angry. If you’re not sure whether you have a temper, ask your friends — but don’t get mad if you dislike what they have to say. _{(Vocabulary.com)}

'Temper' is versatile. It can refer to the tendency to become angry, like the definition says; as well as the state of being angry.

A synonym I like that would be apt here is

spleen

2. Bad temper; spite _(Oxford)

It comes from the old belief that the organ spleen was what caused anger. If your temper causes you to lash out at someone, you're venting your spleen.

A blind rage is where someone is acting in an infuriated manner, coupled with a lack of control or self awareness.

Joe flew into a blind rage when he found out his son had broken his favourite saucer that he'd had since childhood. When he'd calmed down he apologised for acting out of character, and took his son to get ice cream.

Perhaps, fury or furious

fury noun

1 a. violent anger; rage.

b. A fit of anger: "I went into a fury and shouted in his face" (William Least Heat-Moon).

2. a. violent or frenzied action: the storm's fury. b. a violent disturbance or intense period of activity: "The Huns ... moved into Italy, unleashing a fury of destruction" (Arther Ferrill).

3. in Greek & Roman Mythology, any of the spirits who pursue and torment the doers of unavenged crimes, identified with the Greek Erinyes.

[Middle English furie, from Old French, from Latin furia, from furere, to rage.]

(The Free Dictionary)

furor (n.) "rage, madness, angry mania," late 15c., from Middle French fureur (12c.), from Latin furor "a ravaging, rage, madness, passion," which is related to furia "rage, passion, fury" (see fury).

furious (adj.) late 14c., "impetuous, unrestrained," from Old French furios, furieus "furious, enraged, livid" (14c., Modern French furieux), from Latin furiosus "full of rage, mad," from furia "rage, passion, fury" (see fury). Furioso, from the Italian form of the word, was used in English 17c.-18c. for "an enraged person," probably from Ariosto's "Orlando Furioso."

infuriate (v.) 1660s, from Italian infuriato, from Medieval Latin infuriatus, past participle of infuriare "to madden," from Latin in furia "in a fury," from ablative of furia (see fury). Related: Infuriated; infuriating; infuriatingly.

(etymonline)

-phobia, -philia, -mania, seem to be out on their own for compound words

road-rage and

hate-crime ::seem like improvisations to fill the gap.

But fury is nearly out of control:

On 28 March 2013, Lewandowsky published "Recursive fury: Conspiracist ideation in the blogosphere in response to research on conspiracist ideation" https://en.wikipedia.org/wiki/Stephan_Lewandowsky