Hello~It sounds like very dry skin or a reaction to the soap you are using, have you changed the brand you are using lately?
Try taking a bath using the Aveeno bath. This soothing bath treatment for itchy, irritated skin is made of finely milled Oatmeal—this is an ingredient long recognized for its ability to relieve itching. When dispersed in water, this powder forms a soothing milky bath that works as a natural cleanser, provides temporary skin protection, and relieves irritation and itching due to rashes, insect bites, eczema, poison ivy, oak.
When you get out of the tub, apply a good, moisturizer lotion to your legs and arms. A few times of doing this should help clear up the issue.
I have hives when exposed to water. In my case due to having too much thyroid hormone in the blood (even if I don't feel hyperthyroid!). The condition is called aquagenic urticaria aka water hives. This is a rare type of physical urticaria.
Treatments include avoiding the cause (if possible) and anti-histamines.
Excerpt from Wikipedia - Physical Urticaria...
"The cause of physical urticaria is unknown but it has been suggested to be an autoimmune disease. Suggesting that antibodies, which are produced by the immune system to protect humans from foreign microbes, are binding to body tissue; damaging body tissue.[8]
In some cases physical urticaria can be a symptom of an underlying health issue such as:[9]
thyroid disease
hepatitis
infection
cancer.
Or can also be due to:[10]
food allergies
atopy"