A rash which is generalized and appears all of a sudden is mostly due to allergic reaction or a viral infection but for your hands and feet symptoms, pompholyx should be ruled out. The exact cause is not known and excessive sweating can be one of the reasons. But some triggers like allergic reaction to soaps, detergents, foods, latex, nickel etc may trigger the symptoms. Apply some calamine lotion on the affected area and keep the area well moisturized. Use only thin applications of moisturizer ointments as excessive amounts of ointment may restrict breathing of the skin and aggravate the condition.
Topical steroids can be applied but they are available under prescription. Moreover to prevent infection, topical antibiotics may be needed. I suggest you to consult a dermatologist and get it evaluated.
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.