Sounds like you need a deep cleaning. The dental hygienist should be able to tell you the depth of the pockets between your teeth and gum. If they are in the 4-5 range then that’s bad. Inflammation on the gum is a good indication that there are some deep pockets in there. If that’s the case you’ll either do a deep cleaning or floss/brush/rinse more regularly. I think the change in diet may help, but flossing daily and brush/rinse at least twice a day will probably produce better results.
