What Can I Do to Get Rid of the Very Visible Veins on my Back Leg and Thigh. Caused by Bleaching Cream?

You basically have two potential types of treatment, sclerotherapy or topical laser.  Since you have has a problem with bleaching cream, you may want to consider sclerotherapy.  Topical laser always has a risk of laser burn especially in sensitive skin.  You should see someone with sclerotherapy experience.

I am not sure why you were using a bleaching cream. Considering the fact that you have darker skin, you should abstain from using such creams or use them judiciously to avoid HYPOpigmentation (less pigmentation). Nevertheless, the veins were there before you used the cream and they can be treated using sclerotherapy if they are small venules or telangiectasias or topical lasers if they are telangiectasias (spider veins). Seek a Board Certified Phlebologist, also known as Board certified physician in Diseases of Veins and Lymphatics.

Leg veins are usually hereditary. Chronic use of strong corticosteroid creams can thin the skin, thus increasing the appearance of blood vessels. A true bleaching cream should not significantly increase the appearance of leg veins.  Spider veins and smaller varicose veins can be treated using sclerotherapy (injections). Laser is often used for leg veins as well.      Robert S. Bader MD