This long and winding post may be relevant to you. Forgive the presumptuousness if it isn’t.
I don’t do culture shock and I don’t really care where I live, having left my parents when I was 7. I have regularly dealt with severe depression since my early teens. I believe it to be partly hereditary, with an (un)healthy dose of the usual kind of traumas that children often experience.
I have generally been ‘against’ treatment for a lot of my adult life because psychiatrists, counsellors and psychologists are generally horrible, awful and stupid and they did me some serious damage as a teenager, but nowadays, the drugs actually do work. I got to the point where I really didn’t have a choice, though. Good therapists are out there, you just have to hunt around for one that is not mentally retarded…
The causes and the symptoms of depression are not anyone’s ‘fault’, but you can learn to recognise them and manage them so you can feel at peace in your own skin. Part of this is just learning to notice and accept your feelings without judging them. Don’t get into stupid dialogues with yourself; ‘I’ve been in bed all day, I’m so lazy, I’ll never get anywhere, my life is a mess’. That’s wrong. You slept all day because you were ill and tired. Get over it, it’s no big deal. Now smile and go and do something you want to.
All behaviour has its reward even at a simple biological level. You are doing X because you are trying to make Y feel different. The next step is to think of positive ways to change Y, instead of sleeping, getting irritable, drinking, or whatever the X things we don’t want to do are. The real trick is learning how to recognise your ‘Y’s and internalise those new ‘X’ actions.
Consider getting treated for depression. If you are severely depressed, you can’t ‘cure’ it yourself. If you seriously think you are clinically depressed, treatment will give you back your mind, your energy and your intelligence enough to figure out what you need. If you weren’t depressed and were simply in a funk, the process will clear your mind, anyway.
Culture shock is real and it’s hard to figure out whether you are depressed in reaction to your environment or not. If so, changing your environment will help, obviously. My advice to you would be to give yourself a time limit to stay or leave. But really, it’s not such a big question as you think it is. You might be focusing on this as a side issue. Maybe you aren’t, I don’t know you.
Other people
Do what makes you happy. I don’t mean ‘in the big scheme of things’, I mean, right this second. It’s different for everyone. I read, walk in the mountains, take baths, listen to music, write. I used to feel upset when people told me to socialize more, or go and commune with nature, because they didn’t ‘get’ how utterly impossible that was for me at the time. It made me angry when people thought I would lose this racking emptiness by looking at trees, even though I know they were trying to help and reach out. Protect and look after yourself.
I absolutely can’t bear to be around anyone, when I am at my worst. I am pretty awful to be around, also because I feel so fucking awful in every single cell of my body that it is torturous to even look at others. Don’t let other people make you feel guilty about that. You have your needs and they have theirs and if these don’t coincide, get them out of your path. Their needs are probably not more important, at this particular point in time.
When you are depressed, people can and will be cruel and disappointing. This is because they can control their moods fairly easily (so can I when I’m not having a depressive episode) and so don’t always grasp that you are not choosing to be depressed, even though some of the more negative aspects of your behaviour such as apathetic, irritable seem like a choice (‘You will be depressed if you stay in bed all day!’).
At the same time, try to be kind to the people who fail you. Depression has taught me the importance of good manners. Although I fail to be kind to people I don’t like or don’t know, because when I’m ill, I’m the only person I have any sensitivity towards, I know how other people’s rampant arseholishness affects me and try not to do this to others, unless they are on my permanent and non-negotiable shitlist. 
Others will be wise and kind. My best girl poured peppermint tea into me and made sure I ate broccoli and took me to the spa-pool while I stared into the mid-distance and pulled my hair out, strand by strand and understood that the last thing I wanted to do was talk about it. My best boy did my laundry and stood up for me. They made an unbelievable difference.
What you can do for yourself
Exercise is important and has a big effect on your mood but don’t go overboard because you’ll deplete your energy too much if you aren’t eating or sleeping. Moderation in all things is important. Don’t beat yourself up about it if you don’t have the energy or motivation. A ten minute walk or a couple of minutes of stretching is better than nothing.
Drink a lot of water, eat well. No sugar, alcohol or caffeine. Again, don’t beat yourself up if you ‘slip’. Take B vits, Iron, etc. The water is really important; you probably really underestimate how much you drink. It’s boring, but eating and drinking well or badly have more effect on you, physically, mentally and emotionally than you realize. No 7-11 sofa picnics. Record your intake, if this is a problem. Don’t judge yourself, just write it down and note the circumstances that led to the drunken bender, the 6 espressos or whatever your ‘poison’ is.
Entertain yourself with the books and DVDs, trashy TV, films, computer games, make stupid posts on forums, go to look at temple carvings or whatever you like. Don’t feel guilty about this; you need to recharge your body and mind. Make playlists or CDs you can listen to, if you like music.
Relax, if you can. Breathe so your belly goes out and then breathe out, all the way, for as long as it takes to breathe in. Everyone has their own way to relax. I do yoga. I don’t really enjoy it always but it makes me breathe and stretch and the discipline of a routine is good for me.
Journals and lists help you reflect on who you are and what you want. You are not your past, your location, your emotions, your intelligence, your partner, your children, your family, your home, your body, your job, your possessions or anything. All of these things can be wonderful but they can also be prisons. They can also disappear in a flash. You are what you are right now and you can change that, with a little help and self belief.
Treatment
If you need someone to make arrangements for you to see a good doctor or counsellor, PM me. I know that this is an almost insurmountable obstacle, if you can barely get out of bed. The person who helped me most did this for me when I was completely incapable of doing it myself.
TaiDa has some good docs, if you are in Taipei, but you will need to make an appointment. The Community Center in TianMu has some counsellors which may suit you.
Sadness is just a feeling that comes and