Hot Water all by itself can give you dry itchy skin, once you get out and dry off. To minimize this, I tell my customers to add the chlorine after they exit the spa, and only add enough so that there is a barely readable amount of chlorine the next time they go in. This tends to go away as you own the tub and learn to have the levels all just right, and as your skin adjusts to being squeaky clean.
Also you said you are new to this - read the "Chas' Law" note at the top of the forum. Might apply.
8-)