There are a variety of possible causes for smelling a nasty odor not present in the environment. It can be part of an oncoming seizure, or even a weird type of seizure, aura for migraine, reaction to a medication change/withdrawal, brain tumor, etc.
In other words, you're going to have to reveal some of your medical history and any current tests you've had to get more specific ideas. I appreciate you're not wanting to sway people, but at the same time, more signs and symptoms will result in better ideas.
Phantom smell may be due to halitosis(due to infections of the oral cavity or poor hygiene),smell from the sweat or smell due to nasal or sinus infections. As you are having this smell after deep breathing,so it can be due to nasal infection or sinus infection.
I feel that an evaluation by an ENT specialist will be the best. A transillumination test and X-ray sinuses can be done to rule out sinus and nasal infections.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your doctor. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.
I would agree with either halitosis or sinusitis as prime suspects. However, CT of the sinuses would be a better choice than an X-ray. With CT you can evaluate the sinuses better and evaluate for inspisated secretions, erosions, and bony changes of the sinuses that is not possible with an X-ray. Overall the sensitivity for evaluating sinus mucosal disease with X-ray is low, especially if you have symetric disease and no air-fluid levels.
How are you? Aside from sinus infection, post nasal drip, recurrent sore throat and tonsil infection may also be responsible. Tonsilloliths, also known as a tonsil stones are clusters of calcified material that forms in the tonsils can cause the bad odor. These are composed of dead white blood cells, bacteria, overactive salivary glands, or mucus secretions. It is best that you have this checked by your doctor or be referred to ENT physician for proper evaluation. You should also watch out your diet or the type of food you eat since this can also be responsible. Take care and do keep us posted.