I think you have two possible problems.
Breath that you can smell across the room is a dairy allergy or lactose intollerance. Very distinctive smell (not necessarily poo though) that can fill a room with foul smelling breath. It's because your body can't break down the dairy and expels the gas through your lungs as you breathe. Note this folks who say you're gassy or bloated. Get rid of all dairy from your diet. This includes cheese, ice cream, etc. Check food labels to make sure there's no hidden dairy. Remove yogurt also. You can try to add yogurt again later if your body can tolerate it. I know that sometimes I can't stay away from the dairy because I love ice cream. Just know that once you do dairy your your breath will stink for like 3 days. The closer you adhere to this, the fresher your breath. Even a small amount would trigger my dragon breath as my son called it. Interestingly, after I gave up dairy, I lost 20 pounds
in a month. Likely because most items with milk also have a lot of sugars and carbs.
Breath that smells like poop, from what you've said, is coming from your allergies, which could be the dairy issue, or another allergen in your environment.Your lactose intolerance may make your sinuses stuffy and drain down the back of your throat. If you don't clear that daily your breath WILL smell like poop. No doubt. This will make dairy intollerance breath fill a room with the smell of poop. Do a nasal lavage to keep that stuff moving out of your throat. I do two a day. The Netti pot won't give you the force you need. Get the lavage that has the squeeze bottle. Use saline. I also add a teaspoon of peroxide once a day which my dentist says helps my teeth. When you first use the peroxide, you will get the bubbles. It's fighting any infection you have in your sinuses. This will settle down after the first few times. Also a great way to stay free from colds.
This has been my experience. I've vbeen doing this for six years and dentist says my teeth and gums are better for it. The peroxide I mean.
Hope it helps.