Hi,
You answered yourself that question. I quote : "A penis doesn't make me who I am at all."
Most of cis people don't question their gender.If a girl wears trousers then (with time) it will become something that girls do. If a girl does a sport then it will be a sport that girls do. One can question if it is socially acceptable behavior but without questioning their Cisgenderness.
Meanwhile
trans people DO question their gender. And here, in my opinion, the pain starts. The word "DOUBT" is thrown out.
If a transgirl wears trousers then her transgenderness is doubted. If a transgirl does a sport which is not girly, her gender is questioned.
But it doesn't have to be that way. 
If you are a girl and you have a penis, I guess it only proves that girl can have penis.
Self doubt can brings new ideas and open your mind to new possibilities. Being too confident in your belief is not always a way to be a better being. And I like to think that being trans help us to be more open minded / flexible.
Use your doubt to explore yourself, instead of allowing it to create misery.
Maybe you want to be seen as a woman because you are. And you have a penis because you have been born that way. Only you can tell.
Cheers,
