Small spider veins can be improved with a combination protocol that includes pulsed dye laser and microsclerotherapy. You may benefit by waiting until you are older before initiating these treatments.
Raffy Karamanoukian MD FACS
Reticular Veins in Teenagers
I recommend that you get a venous Duplex scan (ultrasound and Doppler) to determine if you have venous insufficiency and start taking bioflavonoids (Varicosamin is a good product). I recommend that you wear stockings If you have venous insufficiency, that can and should be treated with either EVLT, VNUS Closure or ClariVein. Read ebooks provided on the link below.
Hi Joolay. We agree with Dr. Landi's suggestion. For the deeper veins, sclerotherapy is going to be the best option, especially if you are not having any pain, numbness or tingling. If Mom or Dad have vascular issues (especially varicose veins) then this will likely be an ongoing concern for you as the veins tend to recur and also get worse as you age.
For examples of before and after pictures for Orange County, CA vein removal patients, check the link below.
What your picture shows are reticular veins which are blue feeding veins. Since you are only 16, most likely these are due to to a genetic predisposition. There are several options including support hose which I doubt you will wear at age l6. The best option would be sclerotherapy. You should see a vein specialist.