I had chronic swollen lymph nodes in childhood into my 20s, probably. The reason for them was never discovered--since they weren't causing other problems they were ignored.
As for skin problems, I have had sebhoreic (sp?) dermatitis for decades. It was never tied to thyroid issues but perhaps it was indicative of problems that were never found.
I've struggled with weight for about 8 years and had a TT due to follicular cancer with metastasis about 1 1/2 years ago. So now I struggle to find a balance between hyper- and hypo- and it is now even harder to lose weight.
I'm hyper. I had bad eczema as a teen. I've had psoriasis, mostly of the palms and soles of the feet ever since I started taking beta blockers 16 years ago. That's a side effect of the betas.
I also have several allergies to meds. Eczema is very common in the general population. People with eczema often have some allergies. I don't believe there is a connection between eczema and hyper. You'd probably have eczema regardless. I'd look for an allergic cause. Possibily contact. I found out I was allergic to nickel. When I stopped playing the trombone which turned out to be loaded with nickel, I stopped having so much trouble with it. Almost never get a flareup anymore.
My sis has a close friend that has the hashimoto thyroid and she also has eczema. Have no idea if there is a connection with the thyroid and eczema though.