I got to a point where I couldn't bear to actually live or see anyone if they saw me as a guy, and refused to do anything. I had therapy, and anti-depressants, and eventually I got out of the abyss. And when I finally started school again, I realized: I don't have to be a "real" guy; I don't have to make things worse than they are; I don't have to repress my own feelings so much.
From that point on, I quit any remaining attempt or sign of trying to be a "real" guy. I bought all of my jeans and sneakers in the women's department, choosing stuff that was women's, but not too girly (can't exaggerate - not looking for laughs either), carrying an anime messenger bag as a purse (ah, the relief of being able to carry stuff), and growing my hair out. I also stopped trying not to sound too feminine, because not only did attempts fail, but they made me feel awful. And I stopped repressing my own behaviour to a point where I was constantly torn between how it made me feel and how I didn't want to be looked at weird.
And guess what. Of course I was looked at weird. Of course I didn't quite fit in. But every single issue got much better than before. Because I was allowing myself to be myself more, and because happier people attract less crap. I didn't made any more friends than the void I had before, but I definitely became a friendly acquaintance of many of my classmates'. And most of my other issues were toned down because I was locking myself in less.
Now, things weren't perfect, but they became very tolerable. If not for the fear of testosterone worsening things further and further, I wouldn't have yearned for HRT all that urgently. I was almost happy (most of the time, eh), and that near-happiness allowed me to function. Whereas I had quit school three times in a depression, because I couldn't bear my life anymore, I got through a full year of school until I got HRT. And I started a new program, which I liked. And then I went through another year and a half, on HRT (low dose) but still living as a "guy".
People were muttering and arguing about my gender, and to be honest, that was heaps better than them being certain that I was a guy. Even, heck, if I had winter clothes to hide my lack of a feminine figure, beard shadow and hairy arms, at some point I started passing as a girl to almost everyone. Which greatly increased my confidence (it went from nothing to almost nothing - hey, no spitting on an improvement!)
And now, my name change done, my breasts still absent but probably (hopefully) coming in soon after a recent HRT dose increase and my facial hair partly gone (I ran out of money), I'm starting school again on the 26th, as a girl. And the coming-out process will have been made a lot easier by my classmates having already accepted me as a fake/girly guy (gotta admit it did take them a little while, because, well, girly guys are harder to accept than boyish girls apparently), I'm sure.
Now, uhm, birth control pills, as far as I know, are not even remotely useful for you. Those are progestins, right? Progestins' efficiency in trans women is highly debatable, but what's certain is that without estrogen they're absolutely useless. Not to mention that "progestins" that CAN be useful to trans women (according to the half of scientists who think they can be useful to begin with) are not "progestins" as a whole but progesterone, the molecule identical to the natural one. Which I don't think is what you find in birth control pills.
Honestly, it sounds like your parents are still not accepting it fully. They're in denial; they don't want to think it's real. They're angry at you for imposing that "phase" upon them. Eventually, if they're even decent people, they'll come around. And if they're not too poor, they should eventually agree to pay for your medications. You can help them understand, but to do that, you have to be above them. More mature, more patient, calmer, wiser, while not looking down on them. And in your current state of mind I don't think that's possible. And even then, to many parents, the voice of their child has a lot less value simply because it's their "inferior" child. They can't help it; they've been educated that way and it stuck.
The best suggestion I can make is to see a gender therapist. A real professional - a real psychologist for instance - and ideally someone who specializes in gender. Ideally not a psychiatrist, though, because many of them (I won't say all of them, but they're numerous) are a lot more into analyzing you and prescribing you whatever pills might be relevant than doing actual therapy and caring for you.
So anyway, see someone (ideally specialized), who will help you live through things and assess your gender identity disorder. Then once you're comfortable with the therapist and you know they understand you, you can invite your parents to an appointment. Being explained things by a real professional who has all the credibility of one will surely help your parents understand your issues, needs, and the truth and importance of it all.
Also, uhm, one last note. I know it's hard and I know you don't feel like it at all. I know it's near unbearable. But try to find ways to make it a bit more bearable, and start doing something productive with your life. If you manage to make it a bit more bearable and do something that you like, it should distract you from your gender issues a bit and improve your mood.
And uhm, trans or not, whatever the issues, many parents get extremely frustrated by having an inactive child at home, especially if they're adult. Sometimes they exaggerate and don't try to understand enough, but it's understandable in a way: it's extremely disappointing for them to see the child they thought they had raised so well end up in that state. They blame your inactivity because parents like to appear tough like that, but deep down, they think about your unhappiness, too. They probably think they grew up in the "big hard world", back when "you had to work or else", too. Indeed the world was harder in their times in some points. They neglect a lot of the new hardships today's world brings, but well. There's also the obvious fact that they're tending to your needs and they'd like it if you used what they give you for something productive.
Anyhow, I'm not trying to make you feel bad. Just, whether you think they're right or wrong in all or some of their motives or actions, understand that if you are inactive, they'll be a lot less receptive to whatever you might say. If you manage to somewhat get your life "back on track", then I'm sure discussion with them will be a lot more fruitful. That's how parents (and actually, many people) often are. They won't really think logically about whether and how they should listen to you. If they're angry at you they won't listen, and if they're proud of you they will. Well, probably.
It doesn't have to be work. Heck, it can be very devalorizing to work without being in the career you'd like to do, before you can study, if you want to. Not to mention that when you eventually transition, it's much easier to do it at school than at work (generally speaking - there are exceptions of course). The school won't fire you unfairly.
I think your parents are telling you to work because people often assume that when someone stops going to school, school stops being a plan for them altogether. That if you don't keep studying when you're out of high school, it's because you're one of those people who aren't into school at all and want to do a job that doesn't require studies. That's fine if that's your case, too, of course, but you don't have to shove yourself into the mold. Life does tend to be easier for people with a diploma after all.
If going to school is something that appeals to you (forget about being uncomfortable with your body for now), then I'm sure you can have a deal with your parents, eventually, that they would pay for your medication if you do something productive by going to school and by being serious with your studies. Of course, that might require to go through the step of making them undestand your issues and needs better, hence the therapist, but it doesn't mean you can't start school in the mean time.
PS: Oh yeah, and I think you can see it yourself, but indeed, your father is only telling you that out of denial and anger. I have much less of a feminine body than you and before I transitioned, everyone reassured me, telling me how I had soft features and the right attitude (whatever that means xD) and would pass well. Mind you, I don't even have a waist to speak of and I have shoulders broad enough to seriously impair my ability to shop for a coat.
