Might have beckers nevus on my right shoulder. it does look like it however it has been responding to skin bleach. does this mean it may be a birthmar?

Becker's Nevus: There is no effective treatment for the majority of becker naevi. However, the dark brown colour is less obvious if the affected area is kept out of the sun so that it doesn't tan. The excessive hairs can be reduced by repeated treatments with a hair removal laser or by electrolysis. The pigmentation can be reduced by a pigment laser, but this is not always effective and it may also be made worse.

Consider no Rx: All pigmented nevi respond short-term to skin bleach, and skin-bleach will disfigure anything to which it's applied for long. Becker's or not, a pigmented lesion like this might respond to laser rx, or if you prefer you are free to leave it alone -- it's not going to turn to lethal cancer or make anybody sick, and there's a good chance you'll meet someone who'll like it. Your choice.