Sinus drainage can cause bad breath. Try irrigating sinuses with salt/baking soda solution. 1 c. boiled water, 1/2 teaspoon salt, 1/2 teaspoon baking soda, stir to dissolve, strain thru paper coffee filter, fill clean nasal spray bottles, COOL. Do not use until completely cool. At night and morning, irrigate by hanging head off bed, squirt solution into each nostril, sniff, turn head slowly side to side, get up saying "kkkkkk" to keep solution from running down throat. Do not blow nose until absolutely necessary, blot drips for a minute or two. Gently blow as needed. Salt is healing, baking soda deoderizes and is cleansing too. I am not a medical person but my internist has approved of using this solution.
Also gargle every morning and night with Cool Mint Listerin mixed with warm water. Listerin kills bacteria in the throat and tonsil area.
Another cause of bad breath can be infected tonsils and/or food trapped behind tonsils.