While this looks very similar to what I have, the symptoms are not just located on my hands. Dyshidrotic Eczema appears to be mostly on the hands and feet, while mine covers both my hands, feet, arms, legs, pubic area, torso, buttox, and back (none on the face or neck).
I also tried not ingesting medication for a day, and appeared to itch almost as much as I would if I had ingested it. Taking the pills could be doing nothing, and be more associated with a psychological thing than anything else.
From the symptoms and picture,it sounds like dyshidrotic eczema. Wash the areas several times with fresh water. Do not use any cosmetic products at the sites. You can apply some calamine lotion at the rash as it will help in soothing the skin. You can take some OTC oral antihistamine medications like Benadryl or Claritin and see if it helps.
For mild-moderate eczema a weak steroid may be used (e.g. hydrocortisone as dermacort), whilst more severe cases require a higher-potency steroid (e.g. clobetasol propionate, fluocinonide).
Eczema can be exacerbated by dryness of the skin. Use good quality moisturizers to prevent moisture loss from the skin.
If still the symptoms do not improve then pls get a clinical examination done by a dermatologist.
I hope that helps. Take care and pls do keep me posted on how you are doing or if you have any additional queries. Kind regards.