if the reaction in the venting battery produed significant amounts of hydrofluoric acid your delayed symptoms make sense.
hfl can go into your skin and sometimes many hours later start working on nerves and causing pain.
got a tiny drop on my hand doing some glass etching and just washed it off.
later that evening it started feeling like the biggest,meanest,most venomous wasp or hornet in the world was stinging me there.this lasted 2 days.
nothing to do but wait it out.
hope you feel better soon.