One drop will not hurt you, but do not use more or let children have access to the oil. Tea Tree oil does burn. A couple of years ago I had the boil like thing on my gums. It hurt so bad, I wondered if I had an abscessed tooth. In desperation I started putting a drop of tea tree oil on the rising. In about a week it came to a head and masses of puss drained out (yes very gross). A few days later I got another sharp pain in the area and a 1/4 inch piece of either bone or root popped out. After that my mouth healed and I have not had any more problems with that area. Tea Tree oil also healed an inflamed ingrown hair in my eyebrow. Its a wonderful product, but must be used with care.
If you have bacterial or fungal issues in your mouth the Tea Tree oil may help you. For just general use, I don't know if you will see a difference or not; but experiment and try.