Meditation is a great thing to get good at in this world period, IMHO, and certainly can be useful in these kinds of settings, since all it really asks you have is a place for your butt to sit. It also can be truly powerful stress management.
I wish that I could tell you abuse doesn't happen in youth facilities, but it does, and it is just as much of a problem as it is in adult facilities, I'm afraid. And worst of all, it happens more from staff than it often does from peers. I'm sorry to tell you those things, but I don't think it serves anyone very well not to be truthful about this, especially anyone who might be vulnerable to that abuse.
That given, anything you can do to protect yourself, especially passively -- again, you want to try not to set anyone off if you can help it (sometimes you can't, of course, we don't have total control of that) -- is a thing you should do. I'm talking about basic stuff like doing what you can not to be alone with anyone when you can help it, especially anyone who sets your radar off or who has a reputation (you'll probably hear about it from peers) of being abusive or otherwise unsafe. But mostly, I'd suggest that you just pay really close attention to your gut feelings. If someone is making you feel unsafe (particularly, I mean, as you probably will often feel unsafe in juvie, since it's not a place that feels safe or is meant to) or you just feel like they have it out for you, do what you can to avoid them as much as you can, etc. Don't keep any abuse a secret: tell someone, and if you're not sure who is safe to tell, you can start by telling someone on the outside. I'd also say that unless the abuse is or feels like it may come from this wing of things, medical or mental health staff, particularly nurses or counselors, can often be safe people to tell.
Some of this is sounding trite to me because I am trying to cover basics, but also because there's just no making it sound like everything is going to be fine while also being truthful. This is a really hard thing, and while I think you sound like someone who can get through it, it is probably going to be hard to get through, even when you don't suffer abuse, you know?
I'm sorry to hear that you're feeling shame, and I'm also sorry for whatever led you to making this kind of mistake you have to pay for in all of these ways. It might help to remember that memories are short when it comes to high school: it's amazing what people forget very soon after high school that seemed like the hugest deal during high school. Life is a lot more demanding and interesting after high school for most people though, so it's not super-surprising. (I tell you this also as the person who was "that dyke" or "that girl whose boyfriend killed himself or maybe she killed him, actually" and an array of other equally awful assigned identities during a couple years of high school, things that even the people who came up with them from the front very quickly forgot.)
I'm more concerned with how YOU identify you in this than how someone else does. You don't sound to me like someone who isn't taking responsibility. In fact, you sound like you're doing a really good job of that. Maybe just make sure that YOU don't make who you are all about this either, especially when you're in there. Taking responsibility is a thing that can be done without beating up on yourself. Making yourself feel bad about yourself doesn't actually increase the responsibility you're taking, it just puts more stress on you, which benefits no one.
This isn't who you are. This can be a blip: a bad moment you had where you made a mistake, and then the time that came after where you needed to deal with the consequences of it, and maybe accept some of the limits or changes it created (like if you can't start college when you planned). But this isn't who you are, because you're not going to be the kind of person where you make this all of who you are, you know? You can be the person who is about a lot of things, and this is just something you survived and something you learned from..
Never doubt that a small group of thoughtful, committed citizens can change the world. Indeed, it is the only thing that ever has. - Margaret Mead