I am astonished that you have managed to cope as well as you have for as long as you have and to the degree that you have, especially with all of the restrictions that you’ve faced. Well done on all of that, and on wanting your emancipation – and taking your first steps.
To add to the chorus above: No, you are definitely not overreacting. Overreacting, the way some people do it, might involve drugs, risky sex and other associations with dangerous people, or simply running away (or worse, suicide attempts, and worst of all, murder-suicide – those are overreactions). “Not wanting to be controlled” when one is as obviously capable as you describe is perfectly, wonderfully normal. Welcome to adulthood.
As others have explained, you can obtain your own identity documents, and you should have those. If your parents still have access to the places where you might store those for now (such as your college dorm room), or if they can gain access, then it might be wise to rent a safety deposit box at a local bank where you can keep these things perfectly safe from anyone (including college roommates, for example).
Start with your birth certificate, since that will be required to obtain a driver’s license, which can then serve as your primary identification to obtain replacement Social Security card (do you know your SS Number?) and passport.
These mechanical / administrative things are not so difficult. Where you will certainly face difficulty is with your family. Obviously, your mother will be dead set against your steps to emancipate yourself, your father will follow along to get along with her, and your siblings will participate because they have to. So do not underestimate the resistance you will face in trying to break free of these emotional and familial shackles.
I hope that this doesn’t break up your family, dysfunctional as it may be, because after all, it is your family, the only one you have known up to now. But you need to prepare yourself for the possibility that this may, indeed, wreck not only your own relationship with your parents, and with your siblings, but it may put strains on their internal relationships that you hadn’t even considered until now. So be aware that the family could come apart – and be willing to free yourself regardless. Just because the family might split – and I suspect that most of us are in agreement that it might just as well, considering what has already been done to you! – doesn’t mean that you can’t retain or re-establish relationships with anyone you want to (and on your terms!) afterward. But between “now” and “then” you are in for some rough sledding.
I agree that @Seek_Kolinahr can give you some valuable firsthand insight into what you need to do now, and she’s a resource you can definitely use. You might also know some current or former Amish people in southeast Pennsylvania who can describe the “shunning” process that some of them have faced for leaving the flock. That’s the kind of thing that you’re likely to face now.
Good luck to you.