I have super-sensitive skin - I'm using Nivea 50+ for kids this summer - extra water resistant. Comes in a white bottle or 50ml white roll-on so is small enough to carry. No ill effects so far!

Have you looked at sunscreen for babies? Ones sold for babies tend to use minerals rather than chemicals. I'm not familiar with the details of individual products, but there are articles on the internet, e.g. this one: https://www.independent.co.uk/extras/indybest/kids/travel/sunscreens-babies-sensitive-skin-under-over-6-months-reviews-cream-a7672996.html

20 years ago, it used to be possible to buy zinc oxide-based sun screen. It didn't look very attractive but it worked. Another mineral-based sunscreen was titanium dioxide.
These days, as I suspect that my skin is sensitive to the modern chemical-based sunscreens I have been looking for those old type creams. I can't remember the old brand names but they seem to have completely disappeared. I did manage to find a zinc oxide based cream in Holland & Barrett but it's very expensive at £14.99 for 50ml.
An on-line search reveals similar or more expensive prices for other zinc oxide sunscreens.
Does anybody know what happened to the old brands and where they can be purchased at a reasonable price?