Honestly, I don't think this is a stupid problem at all. If people in my personal life found out some of the things I've said on LW... well, it doesn't bear thinking about to be honest! Really, I can completely understand why this is such a big deal for you - so try not being so hard on yourself, yeah? Firstly though, I am really sorry this has happened. It sounds like things are stressful enough as it is for you right now, without your family members finding all your online information now too. The most unfortunate thing is that it cannot be undone. They've seen things now so all you can really do is face the consequences (if there are any) and live with it. I absolutely know that it's not that easy, and it must feel REALLY shit knowing that they know, but there's actually not much else you can do. I would suggest that you make new usernames for whatever sites you do visit, and go back and edit everything you wouldn't want people to see. If at all possible, make future usernames and passwords really difficult to guess and that, y'know? Stop this from happening again. In addition to this, I would also suggest that you just be careful of what you say online. I'm not saying you shouldn't say anything - I understand that the internet can be a really useful way of getting help for certain issues you can't talk about in "real life" - but if there's a chance that this might happen again then perhaps it would be best to make those kinds of topics on a separate account, one that no one will guess is you.
This is a really horrible situation that you're in now, but I'm not quite sure what you want to do now. Do you want to confront your family members about it? Or do you want to continue on like nothing has happened? What I mean is, do you want to confront them about this? They've clearly invaded your privacy, which is completely uncalled for, but I know that if I was in a situation similar to yours, I'd rather not say anything to them about it all. If you do want to confront them, then I suggest that you talk about your privacy and how important it is to you. However, it sounds like your dad and your brother aren't the easiest people in the world to talk to. If you can't have a chat with them, then I think hiding your online identity and making posts as anonymous as possible is maybe all you can really do, in regards to them snooping.
The thing is, I know at the end of it all, it just feels really bloody awful to have your privacy invaded like that. It does feel like you've been violated, and that private parts of your life have been looked at without your consent. It can take a really long time to get over that horrible feeling and to just generally feel better about the whole situation. To have someone look at your private thoughts without your consent is awful and, again, I am sorry that it's happened. Given time, though, I think you can start to feel somewhat better about the situation. For example, my mum read my diary once and I just felt really shit about it for quite a while. To know that my thoughts were shared when I really didn't want them to be. Thing is, there's not much you can do other than accept that it's happened and try to put it behind you, y'know?
As for how your dad treats you in general. Is your mum about, too? If so, how does she feel about how he's treating you? It sounds like you're going through a lot of shit, and you definitely do NOT need his childish behaviour added to all of this. It's not fair or right that he taunts or makes fun of you, especially if you're going through a difficult time right now. If at all possible, I think your mum (or another family member you trust) should try having a chat with him about it. I don't know what your dad is like, so I don't know how he'd respond to that if it happened, so I guess only you can be the judge of that and decide if talking to someone else about it would actually do any good.
Really though - take some deep breaths. You are going to be ok and you are going to get through this. It sounds like going online is sort of an outlet for you (I gather this from what you said about self harming and then going online) so, if it helps, try not to let this hinder you and how you get help. I don't mean to sound so blunt - but hopefully this will help you be more discreet and whatnot (I'm NOT saying this is your fault in anyway, and in a perfect world you wouldn't have to hide things from your family, but the world isn't perfect and if emptying your thoughts online helps, then so be it).
I'm not going to go on and talk about your self harm or anything, unless you'd like any advice for that? I'd be more than willing to give it to you, but as it wasn't the focus of your original post I'll leave it right now. Should you ever want to talk about it though, well, I'm here.
Take care, yeah? I hope you're doing ok.
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it's broken beyond repair. it's in a million little pieces.