Sunscreen definitely works. You're talking to the king of sunburn here. SPF 30 sunscreen has really made a huge difference for me. I used to burn fairly frequently, particularly on snow or at high altitude -- and I wear long sleeves, long pants, and a wide brimmed hat every time I go hiking (well, in the winter I might wear a fleece cap, but sunburn isn't a big issue in the winter).

You definitely can get a sunburn through single layer cotton shirts. To avoid sunburn through clothes, look for clothing with a UPF (like SPF on sunscreen but for clothes) of at least 30.

It's very interesting what can happen when the sun is intense, particularly on water and snow. I got a sunburn under my chin, on the underside of my nostrils, and on the skin above my eyelids, all areas I wouldn't have thought to go heavy on with the sunscreen since sunlight can't hit them directly. Oh, and don't wear really loose, open shorts when walking on snow in spring conditions.

You can also get sunburn through your hair on a high UV day, particularly if you part your hair.