So my experiences over awhile. Got cut up with some live rock years ago. Ended up with a mild fistulous tract (draining tract) on my thumb that caused problems on and off for a year or two. Came to find out there was some tiny pieces of rock inbedded in the area. Was opened and cleaned, and hasn't been a problem since. I work in the veterinary field and clean my hands constantly, even more so during this covid crap. That much washing will dry out your hands horribly and will lead to a rash very similar to what you are seeing. It is much worse in the winter when it's cold and dry, and almost non exsistent in the summertime (unless a lot of surgical procedures are going on). Putting that in saltwater makes it much worse I have found. Best course of action I have found is start lotioning the crap out of the area, keep it as dry as possible. Grab a beer, sit back and enjoy the tank, and keep your hands out for a bit. Would be surprised if it doesn't completely clear up. Also it could be a dermal reaction to stuff in the tank obviously (paly toxin, cyano or other algaes can make toxins as well). Consider UV, ozone, carbon reactor etc.