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Thank you for the question.
Most often eyelashes get drained out of the eye by the tears and do not get embedded or cause any harm to the eye. It is very likely that in your case too the eyelash must have come out of the eye since you do not have any irritation. It is not mandatory to get the eye examined by a doctor if you do not have any symptoms in that eye. The only thing is to be sure that the foreign body which you experienced in that eye was an eyelash only and not anything else. Put lubricating eye drops such as Refresh tears eye drops, 1 drop 4 times a day so as to soothe the eye.