Suffer through it until you can move out if you're living at home. If you're not dependent on your family you should seek out a therapist to figure out how to go forward with your life. At some point you'll want to tell your family, but it can wait until you're more secure and comfortable in your sense of self. But definitely see a therapist, they're a big help.

It all depends on whether you feel very close to your parents to the point of telling them everything. If you don't, you shouldn't tell your family at all, even when you're in a stable situation. Not telling them anything gives you a backup and a place to go back to if you run out of a roof. After that, I don't know your family, but most of the time they end up denying their child. That's what I do with my boyfriend because I have a very conservative family that doesn't accept gays either.
If you are close to your parents or your family, explain to them by doing your best so that it doesn't seem to be something too important, with bad luck it won't help and they will yell at you, with luck they will be at best doubtful or at worst angry without saying anything, with a lot of luck and especially if you explain to them well that it doesn't mean that you are like the idea that they could have of transsexuals, (I know that, "you can't be gay, you don't waddle" it might be the same for "You can't be a woman, you don't wear lipstick, you don't have long hair" etc) they will be understanding.

So are you gonna become a woman or something else? (Or maybe you don't even know?)

(Does that mean we won't have black magekat boy at all? :c I'm really really sad)

Have a backup plan. Start talking with friends to move in with just in case your family is of the mind to disown you when you come out to them at a later date. I also was brought up under an incredibly conservative household (in southern Idaho) and i was dead certain my parents would disown me, so I moved in with my (at the time) mates in Wisconsin. Funny enough tho, when I came out to my parents the summer after I moved away, they were still as supportive as they ever have been. However I was displeased to learn that my mates' liberal parents don't want to even know me because I was "that other boyfriend" in our triad relationship (there's that liberal 'openness and acceptance' hard at work as usual >_>).

I'm not saying that my experiences will be what you should expect, but the bottom line is to have a backup plan and start communicating with friends you can live with that care for you and want to help you and see you succeed in becoming who you want to be, because those are the people that matter in life the most. *offers softbunnyhugs of comfort*

I wish I had words that could guide you through your time, but I don't, so I'll say the only thing that I can think of, Your you no matter how you feel and you are my friend.

As a start, being trans myself. I'd recommend moving at the pace you and you alone are most comfortable with. I'd also recommend reddit.com/r/asktransgender as it's a fantastic support resource. Also, please reach out to me, there's no reason for you to go this alone.