It is very unfortunate that this has happened to you and her, and so early in your marriage. As stated before, when depressed, sex goes out the window. Its not you. Understand you are hurt and bewildered.
I applaud your efforts to spend time with her, to tell her she looks great and all that you do. Keep doing it. She may not seem to be responding, but it is worth your while to reinforce these thoughts to her.
She appears to be fine when with others, etc., because it is easier to fake it with others, and outside of the home, and on the phone. It just is. When at home, with your loved ones, and can let go of the facade, its like night and day. Depression is exhausting.
I think you should approach her about marriage counselling, or couples therapy. This is as devastating to you as her depression is to her. Start out by being calm and saying something about what you said here: "I'm trying to give 110% to make her feel better and support her, but it is getting so frustrating to deal with. I'm on the verge of breaking down everyday and it takes everything I have to not break down and give up. It's very exhausting and I'm not sure how people deal with this kind of emotional stress. It's like I have a roommate that I love and want more than anything, that doesn't even know I exist."
See how that goes. Give her a little time to think it over.
Take the next step and find out where you can get this counseling. Someone you know who's been there, a respected friend, pastor at church, your GP. She may not have the energy to do this. Then tell her that its what you want to do, and encourage her participation. If she won't go, go alone, get started.
And incidentally, some people are not so lucky with meds in that it takes a lot of trying with different ones. It also takes at least 4 wks for them to start working, and there are side effects. but you can still move forward.
Try and get this ball rolling, as the holidays are coming, offices are on a reduced schedule, people's needs for help increase around the holidays. Don't wait.
Hope that helps some.
Again, you are a great husband, sensitive, caring and concerned.
Wishing you success,
"Do something everyday to make tomorrow better."
"One good change creates another."