I havent had issues with my gums but I have had some tooth achiness that wasnt related to cavities or anything. It slowly crept in and is slowly fading away. Id say it lasted fr a couple months.
The swollen gums may very well be due to an underlying infection that is being addressed by the Iodine and your home made gargle. As bacteria dies off it will release additional toxins, gases etc that could be causing a lot of your discomfort.
As fas as "bad teeth" go. If your not already consider a FERMENTED cod liver oil to get a good dose of vitamin A/D and a decent dose of vit K and ample magnesium. There is some interesting info on that combo actually restoring teeth.