Lingual frenulum? That stringy bit at the bottom of the tongue that anchors it to the floor of the mouth? Is it yin or yang? I have never thought about it. But, whether something is yin or yang always depends upon its context. (There is a bit more of this discussed in YinSights
and more recently in this article on What Are The Yin Tissues?
So, what in context would you like to examine the lingual frenulum? In terms of location, it is very superficial, so that would make it yang. In terms of stretchiness (compliance/stiffness), I suppose it is stiffer than most tissues as it is an anchor, so it would be yin. Like with all things, you can ascribe yin or yang characteristics to anything. It always comes down to your intention and the context you choose.
How best to heal a lingual frenulum? I don't know — I would guess that you would leave it alone and let time work its magic
I am not a doctor, but I would be minded to shut up and not talk for a few days to let it rest. Drinking would seem okay, but a lot of chewing might not be great. As always, some mobility is good, but don't over do it. Of course, if you really have a torn lingual frenulum, go see your health care team!