...finally having had enough of the pain and having to keep my finger in water (and having to change the water every 15 minutes as it warmed up) I tried out the lidocaine.
Result: my finger still hurts, but it no longer feels as if someone is holding a hot coal to it. Nor does it feel as if the skin had been flensed from it and it was bleeding profusely, which was another form of suffering I was getting from the thing.
No. It still hurts, mind you, but it's more of the "lemon juice in a paper cut" kind of pain now. Which, let me tell you, is vastly preferable to the "I think it would hurt less if it had been cut off" kind of pain I had before.
Taking stock of the injury: as I said before, a region 1/4" on a side received a 2nd degree burn. There's a small spot nearby which is also burned to that extent, and it feels as if the nail bed was injured, too, which means I'll probably be having to grow this nail back.
Then there's a larger area which received a 1st degree burn. That area covers the entire top (nail side) of the finger from the middle knuckle to the cuticle, making a diagonal line across the the finger between the thumb side of the 2nd joint to the pinkie side of the 3rd.
...this despite my getting it under cold water immediately.
The lidocaine has made it possible for me to get started the loaf of bread I wanted to make; I'll probably still want to defer the apple crisp since moving my finger seems to make it hurt more. The small blister below the main blister hasn't fully formed yet, and that's where it hurts (despite the lidocaine) when I move it. Since peeling apples is finger-intensive I'll be better off not doing that.
It still sucks. *sigh*
Addendum: How much does it hurt to put the viscous lidocaine on the burn? Not at all! Bonus!