DRY SKIN. Yes. Do wash it with a gentle soap. A soap with a moisturizer in it. Dove and tone are good soaps. Cetaphil and aveeno (oatmeal) soaps are gentle. (i have no financial in any of these!) after washing, use a moisturizing cream or lotion.
Yes. Avoid lengthy showers w hot water (warm is better). Oil-based moisturizers hydrate skin. Moisturize skin often. Hydrate well – especially w water. Eat a nutritious diet. Use gentle soaps or cleansers that are unscented & hypoallergenic. Avoid deodorant soaps or other harsh soaps. Remember that you don’t have to wash entire body w soap every day. Use soap on areas that are dirty or where body.
Is it possible to be allergic to being dirty or could I just have very dry skin? I'm always itching all over. Especially when I get hot or sweaty.
More likely dry skin. Try applying moisturizer on skin immediately after bathing to see if this helps. There is another condition which leads to itching and small hives after you get hot and sweaty and this condition may be relieved by taking an antihistamine. If problem persists, see your doctor. (how dirty are you in fact?).