I have had a very similar thing going on the last seven or eight months, although my problem seems to be more the actual nerves being sensitive than just my skin (except for my hands, which I'll get to in a minute). With the exception of the face, I seem to have the problem in the same main locations as you: my hands, forearms, feet, and ankles. I can feel it in the inside of my upper arms, too, if I scratch there.
I will feel a tingling or "zing" along my nerves if I bump them or scrape or rub them (like the "funny bone" feeling but in lots of different places), and I have noticed, like you, that the skin on my hands has gotten much more sensitive. Frequently, if I touch something cold, it feels REALLY cold and almost nerve-jangling, as if normal sensations are highly amplified. Occasionally I am also very sensitive to people bumping into me-- it makes me jerk like I've had way too much caffeine, but it doesn't actually hurt.
I have toyed with the idea of peripheral neuropathy, too, but a physical therapist friend of mine who works with lots of patients and whose father actually has PN has said that it doesn't sound that way to her, so I'm back to thinking that it's just hyper-sensitive nerves. I can't think of any other explanation.
And by the way, the degree of sensitivity that I experience will vary. Is yours constant, or worse at some times than others?
I've posted about my weird thing, too, to see if it is BFS related, and have gotten mixed responses. Some say yes, and that they have it, too (which is immensely comforting), and one person said it sounds like compressed nerves. It seems to go hand-in-hand with an exacerbation of my BFS symptoms, so I feel it is probably related, although I can't really explain it, which bugs me. (I've had twitching for over six and a half years, by the way, and I know I noticed some degree of this sensitivity about five years ago, but it eventually got better).
I feel like I'm in an extreme corner of this disease, too, and I wish I could tell you my symptoms were exactly the same, but they seem to be quite similar. Is it possible that we just have really sensitive peripheral nerves?