I treated it with warm compresses and within a couple of days it started to drain. Here it is just moment before popping.
The entire time I was also checking the inside of her mouth and under her lip to make sure nothing what happening on the inside. Three days after this began, I noticed a hair under her lip. It was so odd looking; I was wondering if it was possible to have an ingrown hair or whisker grow in the wrong direction.
I assumed this had to be the cause of the boil, but the weird thing is that the splinter was on the inside of the lip and at least an inch down from the location of the boil.
Maddie was mostly a trooper through all of this. She dealt with continuous inspections and numerous warm compresses. Her tolerance was rewarded with special treats, of course.
The hair around the wound lost all of the hair because of the drainage. Hopefully it will grow back quickly. I will probably start taking more pictures of her left side for awhile.