firstly.. enjoying you calling an incredibly liberal/accepting person transphobic. Its a pretty telling thing to do...
Secondly.. i've been there and done the trans thing. take your time with it - don't rush into it, and remember a few things:
1, nothing magically changes after you come out.. its a long process if you do go down that route, and you need to be mentally capable of dealing with it - that starts with being stable enough before you set off, something which you don't seem to be.
2, you can express as much 'male' characteristics as you like without transitioning. You have 2 years until your an adult and can do what you like and leave home easily. It may be that the most sensible route is that you just be a really really boyish girl for the next two years, then when your at uni - do what ever the hell you want and your parents won't be able to do a thing
3, Gender non-conformity doesn't mean your transgender.. and mental-pain comes from many sources. Really take your time to question yourself and think whether your pain is caused by your gender, or whether there are wider reasons.
I ask you to think about them because from personal experience, they really matter. It may be that you go through all of it, and then still decide there is no option but to transition - in which case go to your GP and get the ball rolling if you can deal with your parents, if you cant, then wait..
For me, I have always been a bit of a gender-non conformist.. I could easily make the opposite list that you did about girl things.. and when I was going through a really bad time, I was really anxious, depressed and down, I thought the two were connected.. I am feeling awful, and I don't fully conform to my gender? I must be transgender, and this feeling must be dysphoria. After that its very easy to convince yourself that your feelings are real, and painful. No one can question you because only you know your feelings, so its really simple to have people believe you. Turns out for me though it was wrong, I caused myself years more of pain, lost a lot of people, created permanent scars in my relationships with my family, missed some of the potentially best years of my life... all of which led me to exile myself away from everything half of the way around the world. Turns out I am not transgender, I'm just a boy who has a few more feminine tendencies then most boys, and who gets along with girls better then boys.. turns out it wasn't dysphoria I was feeling it was an awful bout of depression with some other mental health issues thrown in, that I would eventually somewhat work my way through.
I wish I could say that I would have listened to myself back then, but honestly - if someone told me what I am telling you know, I would have told them to **** off for being a trans phobic ****.
Still, you can always try.