To add on, I'll try to be t the point; surgery may help you perceive yourself more in your gender, but can never fully determine your gender. No one is going to check and see what you have in your pants, it's all about your brain, what you are expressing, and to a lesser extent, your style of dress and facial appearance, as that's what gives the first impression to others. They often won't key in on your body language as a determining factor in perceiving your gender, which is why most transpeople decide that they need hormones or surgery to change their face and body.
Once again, it's all a matter of your own perception, often influenced by other's perceptions. Hence why we have the term "passing." Do I feel like a woman? Sure. DO I look like a woman? Not really. Do I have the sexual organs of a woman? No. Do the last two impact the first one? TO me, they do a little, to others, it affects them a lot, others not at all. Some, only one affects them. If a surgery helps you feel more like you, go ahead. Some people need these before they feel like them, others just have them to feel more like them, and yet others don't need them at all.
