In the OED side-bar this morning, 3 out of 4 newly published entries begin with "self-":

"Self-applause" — the meaning is self-evident — has been around since the 1600s:

1625 Robert Bolton Some General Directions for a Comfortable Walking with God 126 To proclaime many times with great noise, and selfe-applause, their owne idle malignant forgeries and fancies.
1678 Andrew Marvell Remarks upon a late disingenuous discourse, writ by one T.D. under the pretence de causa Dei, and of answering Mr. John Howe's letter and postscript of God's prescience, &c., affirming, as the Protestant docrine, that GOd doth by efficacious influence universally move and determine men to all their actions, even to those that are most wicked by a Protestant 74 It's Insolent Boasting and Self-applause upon no occasion.

Oh, the titles they had then!

There's also "self-applausive":

1915 S. H. Adams Little Miss Grouch iii. 84 He burst into a paroxysm of self-applausive mirth over his joke.
1941 Booth Tarkington Fighting Littles xiii. 118 The dancers..dropped sittingly, side by side, upon a sofa, screaming with self-applausive laughter.

Hey, "Fighting Littles" looks good — "sittingly, side by side, upon a sofa, screaming with self-applausive..." — especially if you like weird locutions in pursuit of alliteration. But Kirkus Reviews has this pan from 1941:

Let's take Mr. Tarkington around and introduce him to quantities of the nice young things growing up today. I happen to like them, and to think they have more good qualities than he recognizes. He knows his own period- I wish he'd stick to it, for his portrayal of adolescents of the 1940's is distinctly second hand. He cannot streamline Seventeen, reverse the roles (making his Billy Baxter a girl just a bit older and Jane a boy, and insufferable), and make it convincing....

Interestingly dreaming of gender role reversal in the 1941.

"Self-proclaimed" is — obviously — what is proclaimed about oneself, "without authorization or endorsement." This has been around since the 1700s:

1780 Ess. Mod. Martyrs 9 These are the self-created martyrs, the self-proclaimed martyrs, who court the public favour.

Yeah, I know the type.

They've got a 2015 quote there too:

2015 J. Silverman Terms of Service 122 Upworthy is a self-proclaimed liberal site.

"Self-ionization" — sorry, it's not about people. It's about molecules. Doing what-all with themselves.   How'd those little characters get in on Self Day?

ADDED: Trying to understand that 1941 book review, I'm reading the Wikipedia page for Booth Tarkingon. The man was born in 1869 and writing about teenagers in 1941. "Seventeen" was the title of a novel he published in 1916. So he was already pretty old to be writing about what teenagers are really like when he wrote "Seventeen." He was 47. And he seems to have taken essentially the same story and made the boy a girl and the girl a boy when he published "Fighting Littles" at the age of 72. Imagine a man who grew up just after the Civil War purporting to know what was going on with teenagers at the beginning of World War II. They were what we now call "the greatest generation," but Tarkington was saying they were no damned good.

Anyway, he wrote 2 books that you might know from the movies: "The Magnificent Ambersons" and "Alice Adams." He wrote those books in 1919 and 1922 and won a Pulitzer Prize for each.

Tarkington was an unabashed Midwestern regionalist and set much of his fiction in his native Indiana. In 1902, he served one term in the Indiana House of Representatives as a Republican. Tarkington saw such public service as a responsibility of gentlemen in his socio-economic class, and consistent with his family's extensive record of public service. This experience provided the foundation for his book In the Arena: Stories of Political Life. While his service as an Indiana legislator was his only official public service position, he remained politically conservative his entire life. He supported Prohibition, opposed FDR, and worked against FDR's New Deal.

AND: If you're like me, your next thought was, I might want to read "In the Arena: Stories of Political Life." Well, click that link and you can read the whole damned thing:

I guess I've been what you might call kind of an assistant boss pretty much all my life; at least, ever since I could vote; and I was something of a ward-heeler even before that. I don't suppose there's any way a man of my disposition could have put in his time to less advantage and greater cost to himself. I've never got a thing by it, all these years, not a job, not a penny—nothing but injury to my business and trouble with my wife. She begins going for me, first of every campaign.

Yet I just can't seem to keep out of it. It takes a hold on a man that I never could get away from; and when I reach my second childhood and the boys have turned me out, I reckon I'll potter along trying to look knowing and secretive, like the rest of the has-beens, letting on as if I still had a place inside. Lord, if I'd put in the energy at my business that I've frittered away on small politics! But what's the use thinking about it?...

No use at all!