You'd better not makeup your eyes if you are going to take an eye exam. As we know, the makeup will contain a lot of irritating material that may stimulate our eyes. Once our eyes are getting watering. It may affect our true vision after the check. Thus, you'd better clean your eyes and let them do the check.
Yes, you can wear eye makeup to an eye exam, and it would not influence the result of the exam. Due to there are two main eye exam that are general eye exam, which is just checking how well your eyes are. And the other one is prescription eye exam, which could check how well your eyes are after the prescription. The staff would remove your makeup for you if the doctor feels it is necessary. But the doctor usually would only concentrate on your eyes instead of your face. The only thing would make you uncomfortable during the eye exam is your eyes would be watery from looking at the small letters and what they do. Perhaps it would break your eye makeup and make you look not that beautiful.
Personally, it is OK to make up your eyes by using eyeliner and mascara or shadows etc. The makeup is just around your eyes not direct your eyes. So, they won't affect the result of your eye exam. But there is no promises that it wont be smudged or gone by the time you leave.If your really worry about it, you can just take an eye exam first, then makeup.
It seems that you are near sighted that you are gonna get yourself a pair of prescription glasses. Well, since you aregoing to take an eye exam before gettin glasses, you'll need to be relaxed over the exam, and basically, taking an eye exam with eye makeup would not affect you a lot but I still recommend that you take off your makeup. If you must make up your eyes, it doesn't matter and would not affect the result of the test, since the test just involves your eye balls.