Gosh this takes me back to a random and insane outburst of dyshidrotic eczema a few years ago!
Soles of both feet and palms of both hands, exactly like yours.
Had antibiotics, a couple of courses of steroids, and the only thing that really helped (and I still use it now at the first sign of the pomphlyx) is weapons grade DERMOVATE steroid cream. Ask your dr for it, seriously.
I ended up with an infection in my ankle at the time (not via the skin as I never had any spots there, was a bit of a mystery and when I get eczema now on that foot I get a hot and angry red patch on my ankle as a happy reminder), I was on crutches for a time (well sort of, bit difficult with raw palms of hands), tbh I was in a right old mess.
My doctor was aghast at about 3 months in when I told him I was going on holiday to Florida 3 weeks later... cancel my holiday? I don't think so 😎
The flight was agony but the eczema had almost completely cleared up by the end of the holiday! I always wondered if it was the chlorine in the pool that shocked it into submission....? I threw my socks in the bin every day on that holiday 😀
My eczema is seasonal, it starts in April and usually buggers off around November. It doesn't appear every year but like I said as soon as it does out comes the dermovate. This year I have a random stubborn patch on the top of my left foot 🤷♀️
Make sure you keep it moisturised - use doublebase or similar, keep slathering it on because if it cracks it can be really itchy and painful. That patch looks quite dry and cracked on your hand.
Good luck! You're not alone!