Looks like a palmar rash relating to Atopy (Atopic diathesis). This is an indication for family history of allergy.Also called pompholyx. when vesicles(blisters) predominate.
The only thing that comes to mind is that there are different types of eczema. That's definitely not the kind I have, though. I'm not sure what else it might be. As far as that one goes, it wouldn't hurt to look up "foods to avoid with eczema" or "eczema diet" or words similar to that. That doesn't really look like eczema, but the eczema diet might help.
Other than that, even though this still seems different from what I know about things like Lupus, it doesn't seem at all unreasonable to me to get tested for auto immune illnesses. The usual initial blood tests are the same. They test things like ANA and SED rates and TSH (thyroid). What you're going through doesn't seem like a typical auto immune illness, but that doesn't mean that it isn't some kind of auto immune illness.