This is, without a doubt, the most difficult part of transitioning: the time between when you've come out to yourself, and when you are able to to start transitioning. As soon as you've accepted that you need to transition, it's only natural to feel an increased sense of urgency.
Because of your age, it's likely that your mother thinks you're going through yet another phase: her kids have been through umpteen phases over the years and they all tend to fade in time, so she probably thinks that if she just ignores this, you'll move onto something else. The thing is: phases tend to last for 6 months or less, so if you want to convince her that you're serious about it, you'll have to keep bringing it up occasionally so she can see you haven't simply 'gotten over' it.
It's very smart of you to be careful about who you out yourself to under the circumstances. You're right that you're in a relatively weak position in that you don't have the right to choose your own medical treatment, you don't have your own accommodation, and you don't have any income. So the best thing you can do is to sit tight and plan for when you're able to tick those boxes and do something about it.
I see from other posts that you appear to have already experienced the full effects of your original puberty, so you can rest assured that a couple more years of your natal hormones shouldn't do any additional damage. Plenty of guys have to start their transition later in life (I started at 40) and many of us have had excellent results - myself included. I certainly don't look like the ballerina in my profile pic any more.
So what to do in the meantime?
Keep your head down. Concentrate on your school work as much as you can, and take up a hobby to keep your mind off things. If you can, eat healthily & exercise to build muscle and keep yourself trim (this also helps reduce the size of your hips & chesticles). Mention your dysphoria to your mother every month or two, just to keep it in her mind. See if you can coax her into letting you see a doctor or therapist... but if you can't, you know you'll be able to do it yourself as soon as you're ready... so if she says 'no', that really means 'not yet'. Do as much as you can to transition, e.g. hair, clothing, toiletries, name or nickname - and continue with changing your name and pronouns wherever you can, even if only online or with a few IRL friends. And start putting plans in place for what you're going to do to start transitioning. At what age can you get a part-time job, to start saving for your treatment? At what age will you be ready to buy a binder, or a packer? Can you buy a binder & have it delivered to a friend's house, and just wear it when you're not around your family for now? (even a short break from the chesticles can be wonderful).
At what age are you able to seek medical treatment without your parents' consent? (in some places, that's as young as 16). Do you want to finish your schooling first? Do you want to start transitioning before college or full-time work? Once you have some plans in place and a timeline to work towards, it can help you cope with the wait.
And above all: remember that whilst you may feel powerless at 15, you will feel completely different at 25. By that age you will have been working for several years; you will have changed your name & ID everywhere; you will probably have been on hormones for several years & will be indistinguishable from a cis male; you will probably have had top surgery; you may be planning further operations. Who knows, you might even be sharing your life with a significant other.
Bottom line: you'll be much happier in your own skin, and that powerlessness you felt at 15 will be a bad memory.
That's the goal to work towards. Everything you do today will help you achieve that goal, and your 25-year-old self will be
so grateful to your 15-year-old self that you had the strength and courage to persevere.
