Hello.
I felt and still feel as hopeless as you do sometimes, so I can relate on a few aspects.
I think it's going to be hard to transition in that household, the logical solution is to secure your independence, like getting a job and saving up, for starters.
About the gender clinic being far away, I don't think that's an excuse if you really want this. I needed two diagnosis to begin HRT, so besides going to my hospital regularly (which is over one hour away), I took 3-hour trains to a city completely unknown to me, alone. On the days I went, I would get up at 9am and not be home before 10pm... So yeah, who cares how far it is and how long it takes to get there? If that's what you got to do, do it.
Your mom seems very controlling, like mine, but I'm fortunate enough to not have her obstruct my path towards transition. I only just started anti-androgens a couple months ago, and it was actually her that convinced my dad to let me do the medication. I suppose she's coming to terms, though she still asks me to repress myself... But whatever, baby steps, I think that's what you should do too.
Quite frankly it doesn't sound like your mom respects you very much, or your opinion... I don't think that's likely to change unless you show her that you're serious, by working towards your goal on your own without expecting people to drive you around etc.
Also, this sort of thing takes time. It's been two years since I sought out help and I remember being in your shoes, unable to look at other girls, introverted, hiding myself, angry at the world, etc. Things aren't perfect now but they got better, once I realised that even if I wasn't living as a girl yet, I was already alive and there were things I could do. Growing out my hair, dressing in private, laser hair removal, and... Dating. I don't know if the latter is an advice I'd give to anyone, but meeting people in a romantic context helps me. I won't lie, I came out of some situations feeling used, but that's my fault only and I usually don't regret doing whatever I did, because I feel and get treated like a girl when meeting someone. Sort of makes the wait for estrogen less painful and important... Like I'm not me in public, but that there's always someone I can be me to in private... But, that's just me and I how I learned to deal with things.