I grew up in a poor Kentucky farming family and learning to wear sunscreen was lower on the list of daily things to do than wax the Mercedes. I'm now in my 30's and have yet to show any adverse affects and farming all day gives me more sunlight exposure than most. Don't get me wrong, I'm not ignorant of the effects of UV light on unprotected skin, it's just not a habbit I learned when I was young so I do not practice it now, though I'm sure I will when my son gets to the age where he starts asking the question "why should I when daddy doesn't".
The itching does sound more like a reaction from the product though. If you are really concerned bout these things might I suggest getting the Coppertone brand of sunscreen made for children and babies. It has an SPF of up to 50 and contains very little chemicals as possible because as we all know, babies and children are more prone to alergic reactions from such things. You might also want to look into using Banana Boat "After The Sun" cream. It is almost pure Aloe and is a great moisturizer.