You might instead call it malodor, halitosis or fetor ex ore (which is just Latin for “bad smell from the mouth”), but bromopnea is the most technically arcane term for the condition.
If it reminds you of the element bromine, that’s appropriate, since both words come from Greek bromos, a stink (the element was given that name because it has an irritating smell). A closely similar medical term is bromidrosis for strong-smelling sweat. In our case, the second element is from Greek pnoe, breathing, which also turns up in words such as apnoea, temporary cessation of breathing, often while asleep, and tachypnoea, abnormally rapid breathing (pneumonia is a closely related word, from pneumon, lung).
In the UK, the spellings ending in -pnoea are still usual, but the US forms in -pnea are increasingly common, and bromopnea never seems to be spelled any other way.