A trumpet player's lip is swollen from too much rubbing, and the damage changes what the instrument can do. Embouchure is the way a player shapes the mouth against the mouthpiece, so the title points straight at the problem: the part of the body that makes the sound has given out. The trumpet can manage only "a flat" note, which could mean a single dull pitch or simply a sound that falls short of the one wanted.
The second stanza turns to what the trumpet cannot do. It can't "howl" in the "pretty mode recommended / for a fainting fit." That phrase is odd and a little funny, as if there were a polite, approved way to cry out in distress. The speaker seems to resist that tidy, genteel idea of suffering. The mood is wry and frustrated, with a sore, muffled quality. The poem suggests that a real cry is blocked twice over: by a hurt body, and by expectations of how pain should sound.