I had a similar thing happen with my tooth recently. It was OK for 6 months then started to get infected and really hurt. Don't have the cash for the major dental work, so I invested in a water pik, the kind with a special tip to get in the pocket. I just keep it really clean with sea salt water & baking soda, and now the infection is gone (it had spread to my jaw and ear at one point - ouwee!). Some people like to use hydrogen peroxide for this kind of thing. Some people might suggest spraying colloidal silver (not my personal recommendation though, since it will kill the "good" bacteria too).

Certainly fasting will help your body deal with it, although it might consequently flare up a bit at first too (as in a healing crisis). I would stay away from the sugar in fruit juices, and do green drinks if you want to try this. Get on a serious probiotic / prebiotic (like inulin) regime, especially since you took the antibiotics. Probiotics will help to fight the infection. You can even try putting the probiotic powder on your tooth.