Answer
I say, and with God's success: It is not permissible to introduce water into the eyes; because the inside of the eye is not considered part of the face; as it does not face towards it; and because it involves hardship, difficulty, and harm. See: Bada'i' al-Sana'i' 1: 3-4, and Al-Ikhtiyar 1: 13, and God knows best.