Allergy to pool water or chlorine.
You might have dried out your skin. Try using gold bond anti itch lotion.
As it is generalized itch on the whole body,so it can be due to dermatitis(contact or allergic) to the constituents of swimming pool water.Had it been due to the physical contact,then the itching would have been a local one and confined to one area.
Since you are showing these symptoms after entering the swimming pool,so it might be that you are allergic to chlorine or any of the contents of swimming pool.It has been reported that swimming pool water increases the predisposition to allergies and hay fever inswimmers.You can confirm that by getting yourself tested for allergies by an allergist.Skin prik tests and blood tests like RAST are employed to find if you are allergic to chlorine found in swimming pools or any other chemical in the pool.
For your itching pls take an over the counter antihistaminic like benadryl or zyrtec.If symptoms are severe,oral steroids may be needed.Also,if it is your private pool,then ask swimming pool manufacturers to replace chlorine with some other chemical to which you are not allergic.
Hope it helps.Take care and pls do keep me posted in case of additional queries.