Liking (some) stereotypical things from another gender is sign of androgyny and does not confer (nor rule out) a particular gender on the individual -- it just means you don't conform to gender norms.
Transsexual is the term for a male born with a female body (FtM) or female born with a male body (MtF). These people may elect to have corrective surgery, but it's not required in the medical sense.
Transgender is a term that lacks a universal standard, but according to our Wiki and Merriam-Webster (which offer fairly broad definitions), you may be included under this term.
Regarding breasts being a pain, my sister says the same thing. She's decided to accept them for what they are and deal with the bras and such, but it also means she doesn't mind if they shrink if she gets skinnier. Breast removal by itself may be problematic, but a "breast reduction" procedure is not exceedingly uncommon for women. I don't know what conditions differentiate the two from an access perspective, though.
Regarding the idea that being a boy boosts your confidence, this one may take a little while to sort through, so I will offer some theories as to why you get this feeling. The answer may end up being something else (perhaps a bit more subtle), but I've got to put some ideas out there:
1) You may, in fact, be a boy. You don't have to necessarily have to hold hate from getting stuck in the wrong body, but it can still be incorrect. However, if you don't feel the rest of your female parts aren't wrong or simply just don't get that feeling deep down that you are male, then this theory probably isn't going to work.
2) You may be an androgyne (neither male nor female). The possibilities for this term are fairly broad, so I'm not going to try to lay out what they imply.
3) You may be an androgynous female. You are perhaps a girl, but the stereotype of the girly girl is quite far from who you are. You want to do activities because of their merits rather than the gender they are assigned to. Maybe you enjoyed having more male friends because they did stuff that was fun, whereas the things females did may have been less interesting. I myself am male, and I like gaming, computers, and some sports, and I take an interest in math (and applying it as appropriate). However, I don't drink myself stupid, I can handle responsibilities like cleaning the house, and I can juggle psychology and a little dress-up. You don't have to relate to the particulars, but if the general concept holds, you may be androgynous. If you identify as an androgyne, you almost certainly get androgyny for free. Considering that different cultures have their own standards for women and men, what qualifies as androgynous is often relative.
Good luck.
