First of all welcome to the group.
From the picture you posted it is hard to tell exactly what kind of a birthmark it is, but I diffently can tell you about the laser treatment if that is what the doctor is thinking about using. I would say for the size of your birthmark it would take an average of 2-4 zaps depending of the size the doctor chooses to use. Price was, because of the size of your birthmark the appointment will probably take less then twenty minutes, which the laser treatment would take less then two minutes the rest talking. It will probably be a flat rate any were between $100.00 and $300.00 It really depends on the doctor. Being I have not ever had a laser treatment under fifty zaps that I know of the price range I gave you would probably be closer to what you will have to pay.
Also, being that your birthmark is not in a very sensetive area and I do have some of my birthmark in that general area, pain wise will not be to bad. If you are worried about it take a rubberband with you and snap yourself in the arm to distract yourself. I use to do that when I was worried.
Also, If you would like to get a doctors opinion you could look at the front of this website and choose who you would like to talk to and send them an email.
Hope this helps and have a great day.