from bettatalk.com
DISEASE: INFLAMED GILLS
GENERAL INFO: The gill or gills of a betta may become inflamed, because of nitrate poisoning, and possibly bacterial infections, or even a defective gill (if it was born that way).
SYMPTOMS: One or both gills will not close all the way (look at betta from the top it is easier to see it then), gills may look red (inflamed) or not, in the last stages, the betta may be gasping for air, unable to breath.
TREATMENT: Isolate sick betta. Do a full jar water change every third day. Every time you change water, add antibiotic (Pick one that treats inflamed gills) to the water. In the case of nitrate poisoning, simply add one drop of methylene blue in betta’s jar.
hope that helps