A red rash on the hands could be a sign of something as simple as a heat rash or it could be eczema. If it is a heat rash it should fade soon but if not and the condition persists it may be eczema and you should consult a doctor.
If rashes are small in size then use a antiseptic cream regularly,it may disappear. But if they are still remains then it may be associated with an allergic reaction. If in doubt See a physician immediately.
If the rash does not appear to be severe, check online at a website like webmd. com and search similar symptoms. If the rash itches, I recommend using a calamine lotion.