My daughter had the same problem for 3 days. I picked her up from the sitter to notice a fowl smell from her nose. I got a flashlight n looked far up inside her nostrils and found a piece of foam she had bite off and shoved it deep inside her nostril, I was in such panic that I took some tweezers and removed the item myself. Instantly the smell was gone. I assume the smell is from the blocked nostril and the mucus having no way out so it sits in the back of the blockage until removed. Good luck.
It may be bad breath seeming to come from the nose. All my girls got it around this age and it was gone by 6. It is from mouth breathing and when there is an infection it gets much worse. Have they checked to see if she has put anything up her nose? A friend of mine had her daughter put sausage skin up her nose and it took 2 doses of antibiotics before they found it and removed it and then the smell was gone instantly. Good Luck I hope you fix the problem.