Well, it seems that there are some tiny things under your eyes. As a matter of fact, you should not call them milia without confirmation because something they could be fat granules, which are just the similar to milia. However, if the stuff under your eyes are really milia, you could try to remove them through lasik surgery, some hospitals provide such service. Just take a look at it.
There are several causes lead to milia under your eyes. The first one is the sun damage, because exposing to the sun make your skin more likely to form milia.
To stop it, you should wear sunglasses when you're out in the sun. The second cause is facial products. If you use too much face creams or thick makeup, your hair follicles may be closed, leading to the formation of milia. To stop it, you should clean your face after using these products, and you can choose some lighter weight eye creams.
Well, generally speaking, it is normal to have this kind of situation, and there are many people who have this case. So you do not need to worry about it. First, you should know that Milia are deep seeded white bumps that form when skin cells become trapped rather than exfoliate naturally. And for the causes, some irritants, such as the dirty objects, rubbing on your eyes with your hand, can lead to it. For your situation, you can use a sterile small gauge needle to the lesion followed by extraction of the contents. And generally speaking, minimal-to-no scarring is essential. Of course, just check the makeup products you are using, or it can cause them again. Anyway, you can ask the professional to help you.
In my opinion, sun damage is a major contributor to milia, because it thickens and toughens the outer layers of skin, making it harder for dead skin cells to find their way out of glands. The cysts then form in the areas that were overexposed to unforgiving rays.