I am not a dentist, but I have worked in a pediatric dental office for about 9 yrs. Hope I can shed some light. Does she have her two lower front teeth? maybe they are rubbing behind the new teeth where the tissue is tender and making it more tender? A lot of kids grind their teeth until they have teeth in the back for a good bite. The incisive papilla that the dentist was referring to is usually behind the two front teeth right in between them. Not usually behind one or the other. Does she get upset just because you are in there and she is having to be still or is she crying more if you touch it? Also tissue behind newly erupting baby teeth on the top in the front is very puffy or spongey. Also the back of these teeth have sort of a scooped out look and so it is easy for a little one to get something packed in there that can agrovate the tissue. Or maybe she burned it? (don't blame yourself)I would get a soft toothbrush with just water and lean her back good and try to brush softly in that small area for a couple of days. If it did not get better, or got worse I would have a pediatric dentist take a peek! Which she will definately not like!!LOL I am very impressed that you are so observant too!!! Keep it up!!
It could be the incisive papillae. This contains the incisivive nerve. I am guessing at this so I would suggest you her to a pediodontist to be sure.