I have 3 ideas for you that have worked great for us. All are chemical sunscreen free which means they have zinc dioxide, titanium dioxide or a combination of the two as the active ingredients, only. They stay on much longer. The brands are California Baby ( you can find them online & Central Mkt), Blue Lizard (I've seen it at Kroger and CVS) and Neutragena Sensitive Skin (at WAlmart).
Just in case, I know of a good natural mosquito repellent. It is called Buzz Away Extreme by Quantum Health. I got it at Both Worlds Pharmacy on SW Green Oaks (just north of ARkansas) in Arlington, but I've seen it at Whole Foods too.