Girlfriend ignores me and never accepts my apology, even when the issue is her fault. What to do?

I have been living with my girlfriend in Australia for over 2 years now. We share this small house and everything. We are both not from Aussie originally. It seems that every time I do anything remotely wrong, it spawns 2 days worth of crying and ignoring me. Most recently, I nicely asked her to end her 30 min shower to save me some hot water. Eg. "knock knock on door, honey please save some hot water for my 5 min shower? :)". She comes out the door crying and accusing me of treating her like a houseguest. (?). This event comes after I told her something good had happened to me, she tried to turn it into an argument at 7:30am on our way to work. (We don't work together, but leave the same time. She said, "I never make mistakes, so I won't apologize to you!".

Since then (3 days ago), she's been a crabby mood & ignoring my existence even after I cooked her a nice surprise breakfast this morning (to start the day off right). Since moving here (I got to Aussie before her), I have made a handful of good friends. She's been here for 2.5 years, and seems to have put a WALL up to not be able to or not want to make her own friends. She misses her friends from her home country a lot and even once I asked her "would you be happier living in your home country now?". She replied while crying, "no". I said "do you want to move out and go back there?". She said "no" while crying.

So her friends here are who she met through me, but she seems to not have her own set of girlfriends and friends. Get what I mean. So whenever I do something, she comes along or does NOTHING but sit at home stari.

The short of the sad story is that she has been there for me during my dream of becoming a pilot. Recently I achieved that dream and she had been there for me since day one of training to the flight test. I keep telling her that I want to be there for her as well.. for whatever dream she wants to achieve, but she saying "nothing interests me!".

A while back when she was in a great mood, I softened her up for a bold question. I boldly asked if she felt she was suffering from depression. She said of course "I am fine". I told her I'd go with her to a support group because "i love you and just want you to be happy." She declined. Even our now mutual friends (my original friends) seem to say to me (when she's not around of course), "What's wrong with her? She seems distracted, sad always, out of it, etc. Have you asked her about this?". So even they seem worried.

As for a few days ago, the simple act of asking her nicely to save me some hot water for the shower spawned a 'not talking to me, off/on crying, (like summer thunderstorms)' and now it seems she beginning to turn over the framed photos of us which are all over the house. Help!?

I love her more than life itself, but I'd rather have her break up with me and move out than keep doing this to me. Any ladies out there care to help this friendly guy down here with some realistic help and advice?
Girlfriend ignores me and never accepts my apology, even when the issue is her fault. What to do?
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