Makeup remover will not cause damage to your eyes. Before released into the market, products like makeup remover have gone through numerous strict tests to make sure that they pose no dangerous to human health. Your eyes may sting after the remover accidentally slipped into your eyes. Slight redness in eyes and irritation can happen if there is too much remover in your eyes. After you get some remover in your eyes, you can rinse it out with water, and where you rinse should be the eye area, not your eyes. Then use eye drops to flush the remaining remover out. Around 15 minutes later, you will be OK.
Generally speaking, makeup remover drops into your eyes will not affect the development of the eye. But it will cause some discomfort, of cause. Now what you need to do is cleaning up your eyes with plenty of water. Or you can use some eye drops. And if it cannot reduce your symptoms , you can see a doctor.
Generally speaking, it won't. You can wash you eyes by water and then drop a few eye drops. If the next day, you still feel uncomfortable, you can go and see a doctor. By the way, the skin around eyes is very sensitive, so you had better try remover only for eyes.