Burned by laser session. Will this burn fade away? (Photo)

Laser treatments are a medical procedure and you should trust your skin to experts only. I don’t anticipate it to be permanent, if treated and evaluated properly. Nothing replaces an expert opinion and treatment. In the future, Make sure you get the treatment done by a board certafied dermatologist and their team. 

I am sorry this happened to you  
It is important to see what the skin type is and adjust the power on the laser accordingly. You might see hyperpigmentation in the areas that burnt. Eventually they will fade , but sometime this can take several months to years!!
There are things that your dermatologist may suggest you use to minimize the post inflammatory hyperpigmentation. 
I wish you the best!