First of all, I felt so sorry for you. But the good news is, it's no big deal. You might experience some burning or itching feeling at first, (because urine has a high degree of acid content) but do not panic. Flush your eyes with some water (better to be cold water) and have what's left of the baby urine cleansed. If that won't help and your eyes continue to burn, it's high time for you to seek medical help from optometrists. Anyway, good luck.
I am sorry to hear that you got urine in your eyes. You may feel burn in such a situation. Because urine has a much higher acid content than fluid normally in the eyes. So, you shall wash your eyes immediately with clean water. Or you can use your eye drops to flush your eyes. Hope this can help you.
Yes, it is really bad because a bit of baby urine get in your eyes. You should just wash the eyes with clean water and let them out. Then you could just use the clean cloth to dry your eyes. You will feel so comfortable through the warm compress. You could try the warm compress method which will be so useful.