Try stopping the H2Ocean spray and go to a regular sea salt soak. A proper sea salt solution will not dry out your skin. The H2Ocean, however, likely can since you just spray it on and leave it. That lets the water evaporate leaving the salt on your skin, which can dry it out.

I'd suggest not doing anything at all. Just leave it alone.

Moisturize as normal (without getting any on the jewelry).

If it gets crusty or oozie, a warm compress would be fine, but it doesn't even need to be salty.

I find they do best with little effort.