Oil or grease burns on the eyelid skin are similar to burns on any other part of the body. Hot oil in the eye could damage the cornea but the amount that goes in while frying is fortunately not enough to cause too much damage. Firstly, splash a large amount of cold, not room temperature water in both eyes and continue irrigating both eyes for not less than 15 minutes. The blurred vision will reduce once the oil remants wash out but that takes time. Start a lubricating eye drop in both eyes and a good idea would be to refrigerate the bottle so the medication is cold when instilled. Use a preservative free medication like Refresh tears. For the eyelids, use ice packs on both eyes and leave them on intermittently for at least an hour. The pain dramatically subsides and the skin, if it does peel off ,will only be minimal leaving less scarring. You may use erythromycin eye ointment on the eyelids after a long session of ice pack application. Apply a lubricating eye ointment at bedime. You would , at the most, be left with a little redness on both eyelids the next day that will disappear in a couple of days.