One of the possibilities for such symptoms can be an allergic reaction to the herbal medicine. The other possibilities are contact with harsh detergents, soaps and lotions. Sometimes cold, dry air and dermatitis or fungal infections can also cause such symptoms.
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. Use good quality moisturizers to prevent moisture loss from the skin. During the day, hydrate and protect hands with a protective and moisturizing cream. If still the symptoms do not improve then please get a clinical examination done by a dermatologist.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your doctor. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.
If you were taking that supplement to help you secrete heavy metals, then mightn't you have secreted them through your hands the most? Or your body tried to secrete them normally throughout your skin but for some reason your hands stopped them, try checking if the problem exists in the soles of your feet as well, i might just be far flung here, i'm not nearly an expert, but if it exists in the soles of your feet then you know it's not localized at least, and that it's targeting a specific tissue type. I've been told that the palms and soles are quite alike, if medical professional reads this later it would be nice of them to try to correct that for you if need be. But if that doesn't work then definitely go to the dermatologist. If you already went, then can you say what it was? I'm interested now