You know, in a large minority of cases, feet shrink. One, two sizes. There's been pretty amazing results in people over 25 years old sometimes. I think I remember someone mentioning 4-5 sizes. And you might have heard that the curve of effects from HRT and age
is inversely proportional. Waiting one year at the age of, say, 13, will private you of a lot of effect, whilst waiting for one year at the age of 30 will not change much. So with any luck, if you follow the curve, I say that in the hypothetical situation that you start now, you should get at least some relief for your feet.
And what I said above is true for everything. At your probable age (gosh, how I hate that &&%@ age rule), time is of the essence more than any other. You could get fully female hips, a small ribcage, not much beard or body hair to take care of and, most importantly, a normal adolescence. Pretty dreamy in my mind.
So yeah, you should come out as quickly as possible. Your family isn't a bunch of buttholes since they accepted your coming out as bi. So I'm confident they'll at least accept your coming out as trans, if not support you in the process.
But the physical urgency mustn't keep you from using your head to think, not smash through things before taking responsible decisions. So if you feel the necessity, see a psychologist, ideally a gender therapist, and talk about it and make sure it's right for you. See your doctor too, since only they can either prescribe hormones if they're adventurous, either refer you to a psychiatrist for evaluation or endo for hormones.
Though whatever you do, for the sake of your own future, do everything you can to be prescribed puberty and/or androgen blockers as quickly as possible, i.e. before aaanything else, step 1. Those will stop the masculinising damage until you and/or the psychiatrist/therapist/etc. who's evaluating you are ready to start feminisation therapy.
Once on blockers, you can stop worrying, depressing and panicking about how horribly your body is changing, and focus on the real questions about your gender, instead of just telling everyone what they want. You get all the benefits of starting fast, with also the certainty and safety of taking your time. And what's great with those medications is that if, in the end, you discover you're not transsexual and stop taking them, things just resume naturally in your male growth, so it's pretty much a no-brainer. No disadvantages, just benefits.
I say that because if I had been prescribed blockers when I (weakly and obediently ._.) requested them, I would have never had a noticeable Adam's apple in the first place. It appeared while I was waiting on the sadly useless psychiatrist appointments. And a tracheal shave, forgetting the risk of vocal damage, is a good 3000 $ I'll have to pay. And that's the consequence of being stalled for over 2 years when I was 18. Remember the graph? I can't even start to imagine the consequences for you.
Oh, and keep in mind not to do the same mistake as I: make sure you talk to people who can and will give you either a prescription, either a reference for endocrinology/pre-hormones assessment. I was with my psychologist for months and then, when I insisted, she went "trollolol, perhaps you should ask your doctor, because I can't do anything at all for you."
And don't be shy. On one hand, remain polite and remember that doctors don't like to be ordered around, but on the other hand, you need to be insistant and not smile and say "okay" when they say no for blockers. And about the issues your probable transsexualism is causing you, be honest, but not too heavy.
They need to understand it's hard on you, but if it looks like your mental balance might be off, too many professionals (at least mine - and that's already one too many) have a red flag that raises in their mind, and they will want to treat your "other more urgent" issues first, denying the impossibility of the task, since they're caused by transsexualism to begin with.
Good luck, sincerely. I hope you find helpful doctors.
Edit reading your second message: The right time to transition, if you're mentally ready, is always yesterday, especially at your age. During adolescence, I might even say that with the speed and sudden character of undesirable changes, every week matters.
PS: As for your career... I fail to understand how it would even pose the slightest problem to be a trans woman..?