The derogatory expression drama queen designates a person who is prone to exaggeratedly dramatic behaviour.

This expression occurs, for example, in Perfectly pleasant, but low-key set lacks the drama queen we love, by Stephen Dalton, published in the Evening Standard (London, England) of Wednesday 20^th October 2021:

BRINGING an intimate jazz-club vibe to a grand music-hall stage, Rufus Wainwright resisted the urge to play to the gallery at this packed Palladium show. The singer-songwriter, 48, was in a laidback mood, keeping his fondness for operatic melodrama in check as he played a two-act set backed only by a low-voltage chamber-pop trio. Only his sparkly red Dorothy-like shoes hinted at his more flamboyant side.
[…]
There was enough melody and self-deprecating wit in this set to earn Wainwright a rapturous reception, but his high-art drama queen side was sadly underplayed. Glittery footwear aside, this muted show was definitely a long way from Kansas.

Naturally, the expression drama queen is also used to designate a preeminent actress. This predates its use in the sense of a person who is prone to exaggeratedly dramatic behaviour. For example, the following about the British stage and film actress Vivien Leigh (Vivian Hartley – 1913-1967) is from a correspondence from Philadelphia, Pennsylvania, USA, by Joseph Lowry, published in the Daily Herald (London, England) of Monday 21^st January 1963:

VIVIEN LEIGH has made her debut as a musical comedy star—at the age of 49.
She sang and danced her way into the hearts of a packed audience at Philadelphia’s Erlanger Theatre last night.
It was the world premiere of the new musical, Tovarich, and the British drama queen was singing a full musical score for the first time. Dancing, too.

The earliest occurrences that I have found of drama queen in the sense of a person who is prone to exaggeratedly dramatic behaviour are as follows, in chronological order:

1 (?)-: From the television programmes, published in the Sunday People (London, England) of Sunday 5^th February 1978—the acceptation of the expression drama queen is unclear; however, cf., below, quotation 5:

POP STAR and drama queen Marianne Faithfull ¹ joins the panel of Read All About It, BBC1 10.55. A gimmick perhaps, but a pretty one.

¹ Marianne Faithfull (born 1946) began her singing career in 1964, and her acting career in 1966.

2-: From Bye bye, birth pill blues: The cure may be a vitamin pill, by Eve Pollard, published in the Sunday Mirror (London, England) of Sunday 6^th August 1978:

What about the 50 per cent. of depressed Pill-takers for whom Vitamin B6 proves to be no cure? The cause of their blues has not yet been discovered, but research continues.
Meanwhile, if you are among them, don’t suffer alone. See your doctor—he won’t think you’re a drama queen.

3-: From an interview of the U.S. actress Michael Learned (born 1939), by Dick Kleiner, published in The Index-Journal (Greenwood, South Carolina, USA) of Monday 26^th November 1979:

“My friend Anthony Zerbe ² calls me ‘a drama queen,’” she says. “I try to make my life interesting. Sometimes it is something that frightens me. Or worries me. If things are going too well, it gets a little dull. I like to stir things up.”

² Anthony Zerbe (born 1936) is a U.S. actor.

4-: From the following valentine message, published in The Guardian (London and Manchester, England) of Thursday 14^th February 1980:

OH JILLYBEAN, OH JILLYBEAN.

No Crossword ever comes between
Me and my favourite Drama Queen,
And if she fills in all the blanks,
She’ll find my love and thanks.

5-: From Musical notes, by Eliot Tiegel, published in the News-Pilot (San Pedro, California, USA) of Friday 23^rd October 1981:

Marianne Faithful’s [sic] newest LP for Island, “Dangerous Acquaintances,” finds the English warbler in a more mellow mood than usual. It’s also more melodic, she points out, adding that “the root of anger and sorrow has been exorcised” since her previous “Broken English” LP. “I don’t want to be known as the great drama queen of rock’n’roll, though I could have been.”

6-: From an interview of the U.S. model Jerry Hall (born 1956), who was then the partner of the British singer-songwriter Mick Jagger (born 1943)—interview by Noreen Taylor, published in the Daily Mirror (London, England) of Tuesday 10^th August 1982:

“Ah never scream or come all neurotic with Mick. Although mah friends say Ah should act up a bit sometimes.
“Maybe Ah’d get mah way more often if Ah played drama queen.”

7-: From a handwriting analysis made by a graphologist called Diane Simpson, published in The Daily Mail (Hull, Yorkshire, England) of Monday 18^th October 1982:

“A creative lady, used to writing, and fiercely ambitious.
“Very individualistic, a poetic streak appears to manifest itself here and there. She could certainly write.
“A front woman of sorts, whatever her job she is not goal orientated unless it means selling herself as well.
“She likes to underline her own importance, can be a bit of a Drama Queen, will work with other folk, but only if she is allowed to retain her independence.”

 

AN ERROR IN THE OXFORD ENGLISH DICTIONARY?

 

The Oxford English Dictionary (online edition, March 2022), s.v. drama queen, designating “a person who overreacts to a minor setback or who is prone to exaggeratedly dramatic behaviour”, quotes the following from The Washington Post (Washington, District of Columbia, USA) of Monday 10^th December 1923:

If he is thwarted in his effort to enjoy them, he may either go to the dogs or the drama queens, become short-tempered, sullen, grouchy and eventually feel that, in a way he is a failure.

In fact, The Washington Post reprinted a text originally published, under the title The Chances for Father: In the Modern House Some Provision Should Be made for a Man’s Hobbies, in House & Garden (New York City, New York, USA) of November 1923—this original text is as follows:

It is because of no lack of affection for the members of his family that a man wants occasionally to crawl off by himself. There are times when he craves solitude, when he hungers for the chance simply to be by himself, to do what, for the moment, pleases him. Reading, writing, wood-carving, fussing with plants—all these are innocuous and engaging hobbies. A man might be worse occupied—far worse—than in puttering around his room with them. Fortunate is the household whose head is so inclined that he takes pleasure in these things.
But if he is thwarted in his effort to enjoy them, he may either go to the dogs or the drama queens, become short-tempered, sullen, grouchy and eventually feel that, in a way, he is a failure.

It seems to me that drama queen, in this context, does not designate “a person who overreacts to a minor setback or who is prone to exaggeratedly dramatic behaviour”. It is much more probable that “he may either go to the dogs or the drama queens” in this text means “he may either go to the greyhound races or the actresses”—that is to say, he may “be worse occupied—far worse”, as opposed to having the “innocuous and engaging hobbies” that were previously evoked.