You need to change detergent, something mild. You can also use gloves like what Jared mention. Meanwhile, you can make an "oatmeal bath" for your itchy hands. http://naturesnurtureblog.com/soothing-bath-for-eczema-and-itchy-skin/
I think the best way to deal with this is change brands. But if you have no option, use gloves to protect your hands. As for meds, topical antihistamines may work.