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Sometimes peroxide, while mixed with water 50%, can still be a bit "burning" to the gums. While it likely will not hurt you to continue, you may want to back off the mixture ratios, perhaps using 3/4 water with 14 peroxide. It will likely be less caustic to your burning sensation to your gums, and hence less burning throughout the day.
As always, let the majority of your time be with brushing good first, and with part of the time with the 'soft' bristles of the brush angles at a 45 degree angle into to gum sulcus. Then flossing well. And lastly, rinsing good with the preferred mixture, spoken of above. I hope this helps you... ( -:
You mentioned how you were encouraged to see a Periodontist. If you've had gum recession to a small amount, "often" no need for anything. But if it is a moderate or further progressed condition, the Periodontist can add more gum tissue to often reinstate the more desired gum level.
The procedure is called a 'gum graft'. Required having the involved areas numbed, and the donor site (often the roof of the mouth) has your tissue taken from and given to the recipient site (around #8). The donor site heals up & relatively quickly as well.
The site seems to be having some problems(?), but I'm here...
Does the above make sense, as to gum grafting, for gum recession?