According to the Dictionary of Cliches, which I just happened to have on my bookshelf:

Blow Your Own Horn (Trumpet). Boast; extol what one sees as one's own merits. As early as 1576, Abraham Fleming, in A Panoplie of Epistles, wrote: "I will...sound the trumpet of mine own merits." Shakespeare, in Much Ado About Nothing, has Benedick say: "Therefore is it most expedient for the wise...to be the trumpet of his own virtues, as I am to myself".

Two early usages, but hardly the origin.