Now she claiming that I bruised her esophagus
A bruised esophagus is a sign of forced oral sex (or chronic acid reflux): perhaps the girl is claiming Kanye raped her. The more likely explanation, however, is that Kanye is just bragging about the size of his member.
As a total aside, damage to the esophagus can be visualized using a esophagogastroduodenoscopy.
To help improve the meaning of these lyrics, visit “Monster” by Kanye West (Ft. Bon Iver, Jay Z, Nicki Minaj & Rick Ross) Lyrics and leave a comment on the lyrics box