toot one's own horn

toot / blow one's own horn (to praise oneself; call attention to one's own skill, intelligence, or successes; boast or brag about one's own talents) — хвалиться, бахвалиться; хвастаться; трубить о себе; ≈ заливать (в смысле похвальбы себе); ≈ цену себе набивать (в опред. контекстах); ≈ заниматься саморекламой; расхваливать себя на все лады; заниматься самовосхвалением

Example 1:
Joe: I am the greatest person on earth!
Bob: Don't toot your own horn, you ass.

(UrbanDictionary)

Example 2:
Sydney: Well, I don’t like to toot my own horn, but we do have an eighty-five percent success rate of matching couples that stay together for at least two years and twenty-five percent of our couples get married.
Jackie: I guess they are better odds than I’m going to get with someone I meet in a bar or someone my mother sets me up with. (Mv)

Example 3: Our boss always "blows his own horn." He wants everyone to know how wonderful he is.

same as
[blow one's own trumpet]

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To "blow one's horn" is to show off, let everyone know how superior you think you are, to proclaim your achievements, or to claim credit for. It's a rude thing to do and shows arrogance.