There's something in potatoes and pumpkin that draws moisture out of your skin - whenever I make pumpkin soup I try to wash my hands straight away, otherwise the skin goes really dry and stretched. I think I remember googling it and it has something to do with the starch in it? Not sure.
Maybe try give your hands a good wash, and then moisturise them a lot, I'm guessing the itchiness will be because your skin is so dry now.