I have been a fair-skinned person in California all my life, including several years as a lifeguard in 100+ degree temperatures... so I know a thing or two about sunburns! ;) If you are burned, chances are you will peel. That is because the skin is dead and your body needs to slough it off so new skin can come to the surface.
The way I avoid sunburn is to apply a high SPF sunscreen (50+) and LOTS of it. Think of it this way - you should apply a shot glass of sunscreen (that much! really!) at a time. If you are using less than that, it's not enough. Really slather it on. And then, depending upon how quickly you burn, apply it as often as necessary. For me, it's every hour. For my kids (who are blessed with their father's ability to tan), it's every 2 hours. Wear a hat if you can to protect the top of your head, ears, nose, etc, since those areas burn the fastest.
Also, I read an article recently about different brands of sunscreen - it was from Consumer Reports, I believe - anyhow, they found that some of the higher-end brands don't provide the sun protection that they state on the label. The report found that the best brands were Up-and-Up (the Target brand), No Ad, and CVS' store brand. They all provided the SPF that was stated on the label, AND they stayed on the stated amount of time in the water. Good to know you don't have to spend a ton of $$ to get good sunscreen! :)