I have really sensitive hands as well, and I have to make sure I use cotton lined gloves, but I also wear an extra pair of just cotton gloves underneath them.. If my hand are really bad I put on cream before the gloves and also make sure the water isnt too hot...(which sucks as I love to wash in really hot water, but not good for the hands)

I wash by hand now, as I was sick of the dishwasher doing such a crap job and it has now died on us anyway!! hehehe