This has also happened to me when cleaning canisters. I washed my hands well with soap, rubbed in hand cream and that was that. I didn't get any rashes or itching.
Unfortunately, this happens from time to time. We have relatively better conditions for this product. As we still have large stocks of both products, this is unlikely to change any time soon.
The stone gets smaller every day. As its surface area shrinks, its ability to draw water from the air decreases. Shortly before the stone is invisible, you need a new one at the latest. In our case it didn't last 3 months. It was used in the laundry room in the basement.