Yes, the bottles are too large. I am not sure, but I beleive that the aerosol cans are not allowed in the carry on either. I would go to
Walmart, Target, CVS, etc and buy a trail size (or small bottle) of sunscreen. These bottles are small enough (3 oz or less) that you can put them in your carry-on. You sometimes see them attached to a larger bottle of sunscreen and many times the small bottles will have a clip on them so that you can hang them from your purse or backpack.