I had the same problem you had (burning gums and gum sore) not long ago.
I had issues with gingivitis. I used to wake up with my gums feeling fine, but by noon...my mouth would feel like it was on fire. Last time I went for a cleaning was so long ago, I forgot (I'm 24).
What helped me a lot:
eliminating processed sugar from my diet
Pulling with Oregano Oil and Sunflower Oil
adding Iodine to my OP'ing
adding extra-virgin sesame oil to my OP'ing
After reading what happened to sanctuary2, and a post from molly bloom, I won't even go near a dentist (unless the situation is dire).
Try adding Oil of Oregano to your pulls, or switch to Sesame Oil. Since I made the switch, no more stinging gums.