But if I never tan under my clothes when I am in the sun, is it good that I am protected even without UV protective clothing?
Well no, because ultraviolet rays cross the atmosphere whether there is little or a lot of sun, whether it is hot, whether there are clouds or not. Some are visible (UVB) while others (UVA) are less visible (because they are not responsible for the immediate tan unlike UVB). However, UVA rays penetrate very deeply into the dermis and are the cause of spots, wrinkles and skin aging. UVB rays penetrate less deeply into the dermis but are responsible for burns and most skin cancers. Then adopt the right reflexes and protect yourself to take care of your sun capital!