After getting a root canal and crowns done, I have started having bad breath. Will changing crowns help?

Just check the proximal surfaces for any food lodgement in that area. it's my request to upload a photo of your new crown, so I can guide you better.

It is rare but it is possible to have food accumulation either under the crown or between the crown and the adjacent teeth leading to bad breath. You could use a floss or interdental brush to clean these spaces. 
If that does not help, you may have to get the crown removed and replaced with a better fitting new crown.

Hi:There is a possibility that the crown could be the cause of bad breath. However, prior to removal you should consult with a periodontist to see if there is any inflammation or gum issues in any other areas.Best,Dr. Maddahi