When battery acid mixes with sea water, it liberates chlorine gas. If you've got a split battery casing and some acid leaked into the bilge
water...that could explain some nasty burning. (And it is nasty--you don't want to come back without protection.)
In any case I think the process would be to cut exterior power
to the boat, including the AC and charger, then vent the boat thoroughly, and only then come back to see what the problem is. You might very well want to ask at the local fire department (volunteers or municipal down there?) if they have a couple of hazmat guys who can come inspect it with you, because acid vapors can permanently damage your lungs and eyes. They may also have the inspection
tools (sniffers) to tell what the vapors are, and the Scott packs to use for protection while examining the likely suspects.
Since you are docked, and not at sea, why not take advantage of every possible safety
precaution in looking for this?