Whether or not you were raised by your asian mother, the world still treats you like your black and your experiences are colored by being black. The fact that your friends would tell you you "act more asian" or "act white" underscores this. I think you should question whether you want to let your friends define you and disparage those in your ethnic group (one of them), especially to your face.
1. you can check more than one box
2. OP does not mention how the world view him/her. Op just states that s/he does not identify with being black.
Overall it could make an intersting essay or diversity statement. However, I am just curious as to what does it mean to "act white" or to "act asian" ?One can be smart, hard working and not Asian or White.