What can I do about tear trough/veins showing under eyes? (Photo)

Thank you for your
question. Your issue has to do with a combination of loss of collagen support
structure on your lower eyelid, as well as venous congestion due to excessive
capillary overflow in the area. These are best treated with a combination of
facial fillers. Restylane is a commonly used in addition to a non-invasive
laser procedure, in order to reduce discoloration. This dramatically improves
the appearance of dark circles.

The veins that you describe do not show well on the pictures.  Small veins in this area can be treated by sclerotherapy, fine needle radio frequency and possibly topical laser.  Very small veins are difficult to treat.  Bleaching creams may help the discoloration and fillers may soften the hollow areas to lessen the color changes.

The picture your show does not show veins as the problem as the images are not high definition.What it looks like are hollow areas and hyperpigmented skin which is characteristic of the tear trough deformity.I recommend Melarase cream to help diminish this pigmentation and at some point, consider placement of a hyaluronic acid filler like Juvederm or Belotero. However, I am not convinced that you need fillers.