Visible Blue Vein After Fillers?

Depending on which filler was used, that blue bagginess under your eye may be the result of the filler.  If that's the case, then that might be completely reversible with a subsequent injection of hyaluronidase.  If the filler was one of the hyaluronic acids, I would discuss this with your doctor.

Sorry to hear about your problem.  It sounds like you may have developed the Tyndall Effect.  This is a fairly uncommon reaction some people get to fillers, most often hyaluronic acid-based ones, that are injected into the thin tissues under the eyes.  The scattering of light from the injected filler can cause a bluish discoloration.  It's been described in the scientific literature multiple times, but is not common in most other areas of the face (like the nasolabial folds).

Most physicians treat the Tyndall effect by injecting hyaluronidase, a substance that can be obtained from compound pharmacies.  It can dissolve the hyaluronic acid filler away, but may take more than one treatment.  I encourage you to see a reputable, board-certified plastic surgeon, facial plastic surgeon, dermatologist, or oculoplastic surgeon to check it out. 

Good luck.