If you’re like most people, you usually don’t step out into the blazing-hot sun unless you’ve slapped on a good amount of spray or lotion to ward off the cancer-causing UV rays that bombard us when we go outside. And for many among us, this isn’t simply a case of slathering on sunscreen when we head to the beach or to an outdoor all-day picnic—no, we need the stuff daily for our day at work, school, or simple outdoor recreation.

But according to new research from the U.S. Food and Drug Administration (FDA), the chemicals in our sunscreen don’t merely sit on top of our skin until we rinse it off. Instead, many of the active ingredients enter our bloodstream at levels far in excess of what was previously believed...