Kate, I can't speak to the eczema, I've never had that. All I've had (and still have) is recurrent outbreaks of fungal skin infections that may or may not be connected with SS. It's probably not the same thing - the distribution sounds wrong - but fungal infections do produce a hot, red, itchy rash.
However, peripheral neuropathy is a well-known feature of SS. I had exactly that arm thing you described for years, and sometimes woke in the night with one or other leg completely numb from the knee down. And one of my earliest symptoms - nearly 20 years ago - was an unbearable tingling sensation in my right big toe. The toe eventually became almost completely numb and stayed that way for 10 years, with the development of an excruciating electric-shock sensation in the skin over the nerve leading from my big toe up the inside of my instep. (I dreaded washing or drying my foot for years.) My doctor wasn't interested - just said it was down to old age. I was 53 when it started.
Then the weirdest thing happened. From one day to the next the numbness and the electric-shock sensation vanished completely. Just like that, and after 10 years! I'm a former nurse, specialised in neurology, and I "know" long-standing nerve damage like that can't disappear overnight. But it did. And then it got weirder...
That same night, I was woken by a terrible tingling... in the other big toe. (I'm not making this up!) That moment, at 3 in the morning, was when I fully understood the psychosomatic aspect of auto-immune diseases. After all, it is a form of self-destruction - the body turning on itself - and I've long known I had a self-destructive element in my psychological make-up. I put the light on, pushed off the covers, sat up in bed and announced out loud to the offending foot: "No, we're not doing this!" Then I tried to get back to sleep. The sensation cleared up after a couple of days and never came back in either foot.
In the five years since then I've been in almost total remission. Before that I had dry mouth, dry eyes, arthritis, Reynaud's syndrome, carpal tunnel syndrome, as well as the peripheral neuropathy. All I've been left with now (at age 70) is an underactive thyroid, for which I take thyroxine, and the occasional rare attack of dry mouth or sticky eyes.
You're not turning into a hypochondriac, but you're on the right track in suspecting you might somehow, at some mysterious, inaccessible level, be influencing your own symptoms. Just hang onto that thought and it might work in you. Psychosomatic illness is not imaginary and it's nothing to do with being a hypochondriac. It's way more subtle than that. People die of psychosomatic illnesses. Just let your rogue immune system know you're on its case and you might be surprised by the results!