As easy as it would be to say "screw your parents, you're old enough to do what you want, if you feel that you need to start HRT and transition then do it"..... that's not realistic, at least in your case.
What is realistic is that you don't have your family's support, and you don't have any money saved up as a safety net in case things don't work out. $300 will start you on T, i bet, but won't last you through the frequent check ups and blood work you'll need the first year - and certainly won't pay for a place for you to stay if your parents kick you out. Or for your car. Or college.
You need to think it through very carefully, considering what you have to lose. Roof over your head. Food. Warm and safe place to sleep. Schooling. Transportation. It's a lot to lose, considering you could wait a year for HRT and in the mean time take other steps towards transitioning: like finding a gender therapist and working through some of these other issues, maybe working your parents around per suggestions from the therapist... or even finding a job with good insurance.
I came out when i was a little older than you are now. That was in 2010/2011. I didn't start HRT until four months ago, been in therapy a year now. Not saying you'll have to wait anywhere near as long as i did (i had other things to worry about - my health, career, etc). Point is, there is no rush even if it feels like there is. When i made the decision to transition years ago i was ready to start T ASAP, thought i would be on it within a year and have top surgery and change my name.... doesn't always work out as fast as we want or hope, but that doesn't mean we should give up entirely.
Point is: i think focusing on becoming independent of your parents should be priority. Get a job. Good insurance. Find a gender therapist. Work your way up to HRT. There is no rush. There is no shame in choosing to focus on other things that may be (in this case IMO ARE) priority.
In regards to actually getting T - you won't get in to see an endo without a referral from a therapist. Some clinics will also require that referral. A lot of medical professionals are NOT keen to prescribe T to anyone who hasn't been to see a therapist first. It IS a controlled substance and VERY powerful. They do not want to prescribe it to someone who is going to misuse it or "change their mind".
Having a GP or a clinic like planned parenthood do it is, IMO, risky as you do not know if they're knowledgable enough to be prescribing safely. I've heard some prescribe without requiring follow ups or blood work which is a BIG no-no. My GP wouldn't do it.
Good luck.
