Pink eye is not caused by farting on someone or farting on someone's face.
Although it's disgusting for someone to fart on your face or fart in your eye it's not a cause of pink eye.
If you got pink eye after you got farted on in the face then it's not because of the fart but because you were likely around someone who had the virus or bacteria that causes the pink eye.
Pink Eye is a contagious medical condition but it's caused by bacteria or a virus and not farts.
Farts are not harmful to you other than making you gag or throw up and farts consist mostly of and is primarily methane gas and does not contain bacteria that can cause pink eye or other health conditions.
If you do have pink eye you should stay home from school or work and avoid touching your eye.
There's not much you can do to get rid of pink eye once you get it and in most cases the pink eye usually goes away on it's own without any treatment.
But you can use eye drops that contain antihistamines or by using some pink eye home remedies such as applying warm or cool compress.
Pink eye lasts from a few days to as long as a few weeks.