A careful Evaluation is needed

 You need to have a careful evaluation by an experienced laser surgeon to determine if the veins are treatable.  Many blue veins around the eyes can be treated safely using pulsed-dye lasers. The decision is based upon size primarily, and somewhat by location.  Expected side effects from these treatments are bruising, multiple treatments and only minimal swelling or discomfort.  I recommend you see a board certified and experienced dermatologist, facial plastics,  plastic surgeon or oculoplastic surgeon with extensive laser experience for a thorough consultation.