Hi Buttons, and welcome!
As you've discovered, Gender Dysphoria does not get better on its own: it gets worse the longer you ignore it. Many of us here have lived with it for many decades before transitioning, but hopefully you'll be luckier and will be able to start your transition sooner.
If you're not yet financially independent, you'll need to consider whether your need to transition is more urgent than your need to graduate. Many of us had to postpone our transitions because we had other commitments... such as education, jobs, marriages, kids etc. It's hard - very hard - but you need to look at your big picture & decide what your best course of action might be. If it were up to me, I'd take a fiendish pleasure in making my parents pay for my expensive education and setting me up for a good start in life, knowing that I was going to begin my medical transition as soon as I got my first job. Thinking of the megabucks I made them spend on my education would make their possible rejection that much sweeter. But that's just me.
Is it possible for you to do some work towards your transition whilst at college? There's plenty you can do to start your social transition, even if you know your folks won't pay for you to start your medical transition. You don't say whether you live at home or at college, but you might be able to femme-up your presentation whilst at college and then change back to boy mode when you go home.
You could start with simple things like buying & wearing female undergarments that your parents don't see (careful how you wash & dry them!), or painting your toenails, or wearing ladies' deodorant, or growing out your hair into an androgynous style, or getting your ears pierced, or asking your friends to call you by a female (or gender-neutral) name rather than your birth name. You could ask a friend to teach you how to do make-up & hair. All of these things are wonderfully self-affirming and they can help you cope whilst you wait to begin your medical transition. However, I should warn you that transitioning tends to have a snowball effect: once you get started, your need to go further can become even more intense.
Does your college (or town) have an LGBT society you could join? There may be other trans people there who could give you the vital support and validation you need. If you are in the US, could you talk to Planned Parenting about the possibility of going on hormones via Informed Consent? You could also speak to your family doctor... as long as you can be confident that they won't inform your parents about the contents of your conversation.
Your folks, of course, are at best misinformed and at worst deluded. But at the end of the day, it doesn't matter whether your father 'believes' in mental illness or thinks that being gay or trans is a choice: his 'beliefs' don't amount to a hill of beans in the grand scheme of things, and very soon you'll be fully independent of him so you won't have to trouble yourself with his views if you don't want to. At your age, you've spent your entire life under your parents' thumb and you're used to their word being gospel (pardon the pun). But the instant you move out and start your own independent life, you will be in charge of your own destiny and they won't be able to stop you from doing what you need to do. Hold on to that thought. [hugs]
Your use of terms like 'college' and 'MCAT' lead me to suspect you're in the US: most of our American friends are tucked up in bed at the moment but I'm sure some will be along in a while to give you more specific advice.
