Hi Bassinga, it sounds like you're feeling really alone in all of this (although you do know we're here for you!!). While I'd say it might be a good idea to tell your parents regardless, I'm guessing they really care about you??? It's still really important for you to have something to "fall back on" if you get the urges to SI e.g. writing, talking to someone, distraction, something active..........whatever might help you just a little. I can completely understand how hard it might be if your parents did take away........but if you've got a back-up plan (other than SI) that might help a bit.
But if/when you tell them, it shouldn't really be as simple as you SI, just make sure you tell them the feelings (and sometimes lack of feelings??) behind it and how it makes you feel if you can't SI. That way they may be able to understand what you're going through a bit better without the means to SI and give you some extra support with that.
For the feeling of being disconnected though if you're feeling depressed you aren't going to be really "connected" so don't make that all about being a problem with you. Maybe instead look at some (more?) really small connections you can make. Connections that don't involve pretending you/things are different than they are as that's likely to make it even harder for you. Perhaps just try to be with people a little more, share something more (an activity?) however little it is with them, do somethings for them, ask them to do somethings for you, talk about things you've shared in the past/your relationships with them...............and maybe start to try to let people in a little more about how you're feeling??
But don't beat yourself up because you don't feel "normal" or because things aren't like they used to be for you. You're feeling depressed/you are depressed it can be a bit of a journey to overcome that with some help and support along the way. So cut yourself some slack!! And instead focus a little more on the things you can do/you are doing to get to where you want to be. Don't be so hard on yourself!!
And if you've managed to stop drinking, which sounds like it was hard for you, you've absolutely shown you've got a lot in you/a lot about you!!! I know things seem/feel really hard for you right now but don't forget you've got that!!!
Best wishes
Alison