This slow time-course does not sound like either acid; certainly not conc. sulfuric. The lack of visible contamination on the gloves is suspicious. The slow growth generalized irritation/necrosis is suspicious.

How about the wastewater the lab was studying. Getting a small splash is not threatening, after, "it's just water."

The circumstances could easily bias the Dx toward chemical, when if fact, it is microbiological.

I think there are way to many unknowns to do more than speculate, and it is too late to get a verifiable determination

Work safely - the skin you burn may be your own!