"and how little Fanny came by that whitlow: "
I never heard this term used. I have heard "felon". Both uncommon now with ready availability of soap and running water.
Webster's 1913 Dictionary

Definition: \Whit"low\, n. [Prov. E. whickflaw, for quickflaw, i.
e., a flaw or sore at the quick; cf. Icel. kvika the quick
under the nail or under a horse's hoof. See {Quick}, a., and
{Flaw}.]
1. (Med.) An inflammation of the fingers or toes, generally
of the last phalanx, terminating usually in suppuration.
The inflammation may occupy any seat between the skin and
the bone, but is usually applied to a felon or
inflammation of the periosteal structures of the bone.

2. (Far.) An inflammatory disease of the feet. It occurs
round the hoof, where an acrid matter is collected.

{Whitlow grass} (Bot.), name given to several inconspicuous
herbs, which were thought to be a cure for the whitlow, as
{Saxifraga tridactylites}, {Draba verna}, and several
species of {Paronychia}.