No, the DermaJet is not very suitable for this sensitive part. The upper and lower eyelids have the thinnest skin on the entire body. In fact dark circles are mainly caused by the fact that the skin is so thin. The underlying tissue such as veins and the orbicularis oculi muscle shine through as bluish, reddish or purplish tones. In addition, because there is not much fat between the skin and the muscle, the dark muscle absorbs the light and that makes the area darker.
Buy a 0.5 mm dermastamp and use it gently up to three times a week in that area to hopefully thicken the skin.
How to roll or stamp around the eyes. Please read my reply #2:
https://http://forums.owndoc.com/dermarolling-microneedling/can-i-use-a-dermaroller-on-this-area-under-the-eye-(pic-included)/ Related forum thread:
https://http://forums.owndoc.com/dermarolling-microneedling/derma-stamproll-to-thicken-very-thin-under-eye-skin/msg5037/#msg5037 Milia should be extracted.
Milia consist of keratin - the skin's hardest protein that makes the outer skin layer so tough. Hooves and nails are also made of keratin.
You can pierce a milium with our single needle (start with making one or two pricks into it - it should be enough) and extracting the entrapped keratin by very gently pushing it out with two paperclips.
Salicylic acid has a keratolytic effect (softens keratin) - it would be useful to apply it on the milia before needling and extraction.