Crown on a root canal fell off. Am I allowed to disinfect with mouthwash without hurting the exposed gums?

I agree with getting to the dentist. If you are having malodor, it could be due to the infection, but also other issues within your mouth you could be unaware of like periodontal disease.The mouthwash isn't going to hurt anything, but it isn't going to do much besides masking the odor for a short period of time.

It isn't a problem to rinse with medicated mouth rinses to keep the area clean. I suggest getting into your dentist ASAP to have this evaluated.