Is the sunscreen waterproof? If so, rinsing the eyes with water will not get it out. But do not be panic. You can drop artificial tears in her eyes to flush the sunscreen out. Artificial tears are really useful. You can buy a bottle of it and take it with you wherever you go with your baby, for babies are so careless that they can get anything in their eyes. If your baby still has painful sensation in her eyes, you should call the poison control center for help. Sunscreen may irritate the eyes, but any kind of sunscreen produced by reputable manufacturers will not cause permanent blindness. So you need not be too scared.
It is so dangerous for your little baby to get the bit of sunscreen in the eyes which could cause the problems of eyes. You should help her wash the eyes with clean water and dry cloth. You should do it gently to get the sunscreen out of the eyes. The warm compress is also a good method for you to do for her. You could have a try.
Sunscreen is a kind of chemical synthesis agent, which can absorbultraviolet rays and prevent the ultraviolet rays from penetrating through the skins, so as to avoid the damage that the ultraviolet rays can do to the skins. In your case, you can just use flowing and clean water to wash the sunscreen out of the eyes, and then apply some moderate eye drops that are specially intended for children's use to the eyes of your little baby, which can be helpful in easing the discomfort in the eyes. In addition, after that, you had better put the baby away from where there is powerful sunshine or strong light, in case that the eyes of the baby get irritated again. If needed, you can let the baby take in some vitamins such as vitamin A and vitamin C, which are good for the eyes. But if there is red eyes or other kinds of eye diseases, you had better go to the doctor's for medical treatment.
I feel so sorry to hear that. The sunscreen contains several kind of ingredient such as Avobenzone(Parsol 1789),Titanium Dioxide,Zinc Oxide and some others. These chemicals will cause sting or irritate your baby's eyes. Once it accidentally get into your baby's eyes, please wipe the eyes and hands clean with a damp cloth and call the pediatrician as soon as possible.