E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
To trumpet ones good deeds. The allusion is to the Pharisaic sect called the Almsgivers, who had a trumpet sounded before them, ostensibly to summon the poor together, but in reality to publish abroad their abnegation and benevolence.
You sound your own trumpet. The allusion is to heralds, who used to announce with a flourish of trumpets the knights who entered a list.