The Beatles were a pop and rock group from Liverpool, consisting of George Harrison (1943-2001), John Lennon (1940-1980), Paul McCartney (born 1942) and Ringo Starr (Richard Starkey – born 1940).
—Cf. ‘grotty’: meaning and origin.

The noun Beatlemania denotes:
– the frenzied behaviour of the Beatles’ admirers;
– addiction to the Beatles and their characteristics.

The noun Beatlemania occurs, for example, in an article by Samuel Fishwick, about the British singer and musician Alex Turner (born 1986), the frontman of the rock band Arctic Monkeys, published in the Evening Standard (London, England) of Thursday 20^th October 2022:

2014, a time when the Arctic Monkeys had finally broken America and were met with something close to Beatlemania in Mexico.

The earliest occurrences of the noun Beatlemania that I have found are as follows, in chronological order:

1-: From the column TV as I saw it, by Maurice Richardson, published in The Observer (London, England) of Sunday 13^th October 1963:

The Mersey Sound, Don Haworth’s programme about the Beatles and allied groups of performers and the whole phenomenon of the Beatle boom, was an excellent little documentary. Light and fast yet packed with significance, it gave you a strong contemporary feeling. The degree of Beatlemania, with fans sleeping under Beatles’ windows and sending them jellybabies by the ton, seemed to be fairly acute.
One of the odder features was the extreme youth of many of the fans. Some of them were barely out of the toddlers’ group. This was especially noticeable when they swarmed round a Beatle on his way out of his house. They seemed to be identifying closely with him as one of their own kind rather than as a mere teenage idol. He was almost visibly filling some gap in their forlorn little lives. The Beatles themselves made a distinctly agreeable impression. They weren’t exactly modest but they were quite free from megalomania and perfectly prepared to face the possibility of a short reign before oblivion set in.

2-: From the Evening Chronicle (Newcastle-upon-Tyne, Northumberland, England) of Friday 25^th October 1963:

BEATLEMANIA
That’s why the fans are in a queue that will last two days

The Beatles are coming—and just dig that crazy queue!
Tickets for the swinging pop group’s Newcastle concert will be on sale on Sunday.
So today seven “with-it” Tyneside fans began a two-day vigil on the doorstep of the booking agency in Newcastle.
Sound…
Reason: They want to get tickets for the front seats—so that they can hear that Mersey beat.
Schoolgirl Shirley Chrystal, aged 16, said: “If anyone screams, I’ll go mad.
“Anyone who thinks we are camping on a cold pavement for two days just to see their handsome looks are mistaken.
“We just like the sound they make.”
Sweaters
Four girls were driven to the agency in Saville Place by their fathers.
One was wearing jeans on which she had painted the Christian names of the Beatles.
They came well prepared for the long wait with sweaters and duffel coats.
For it’s going to be cool tonight—real cool!
● The Beatles concert is at the City Hall on Saturday November 23.

3-: From the Birmingham Evening Mail and Despatch (Birmingham, Warwickshire, England) of Saturday 26^th October 1963:

‘BEATLE-MANIA’ IS SPREADING STILL

“BEATLE-MANIA” spread to several new parts of Britain today. At Carlisle, Cambridge, Bournemouth and Hull, police were called out to control screaming fans of the country’s top “pop” group.
Church windows were smashed by beer bottle throwing teenagers queueing for tickets at a Cambridge theatre where the Beatles are appearing on November 26.
The church stands next to the theatre.
Police warned the crowd, which had been growing in size since Thursday and early today reached 1,000, that further damage might lead to arrests.
At Hull, about 2,000 teenagers queued all night outside a cinema waiting to buy tickets for a Beatles show next month.
Screaming fans
As the queue grew longer, extra crush barriers were sent for, and by daylight 50 policemen battled to control the singing, screaming youngsters.
Police had to struggle to control a crowd queuing to get tickets to see their idols In Carlisle.
The teenagers—over 600 of them—had come expecting to stay the night on a pavement near the cinema in Warwick Road, which the Beatles are visiting soon.
Sleeping bags, vacuum flasks and transistor radios were the order of the day—and night.
Police managed to keep good order as the queue lengthened to over 500 yards long. Suddenly a rustle went along the queue, girls screamed and patient fans turned impatient.
The queue moved forward and people at the back started running forward.
Police joined hands, but the cordon started moving in the centre. The crush got worse and ambulance men reported nine casualties.
Cinema manager Mr Neil Scott Buccleugh opened the box office and a race began to see who could get their tickets first. The crush got too much again and three panes of glass in the cinema were broken.
Then, as suddenly as it had opened, the booking office closed. In one hour, 2,000 tickets had been sold.
Unsuccessful Beatles fans wept. There was still a crowd of 200 waiting, and it took police over an hour to disperse them.
50-hour wait
More than 60 policemen battled to control a crowd of 2,000 Beatle fans outside Bournemouth Winter Gardens. Many had waited 50 hours to buy tickets for November 16.
Sleeping bags littered the ground and portable record players pounded out Beatle hit tunes. Three girls in the front of the queue fainted.
Meanwhile, the Beatles themselves were at Karlstad, Sweden, where they had a fairly quiet reception at the start of their Swedish tour.
Two or three young Swedish girls who tried to climb on the stage were defeated by their tight skirts. Two youngsters started to dance the twist during the Beatles’ performance, but when police pointed at them they sat down again.