People don't mind read, and they don't know what's going on.  If you don't tell them, then you can't expect them to know, and you can't expect them to respond properly.  Your doctor was dealing with you, and you could have outright mentioned what you felt was the case.

And while that's never easy (I have the same problem) I don't think you can hate someone for not knowing or understanding you.  It's very typical of teenagers to go through these stages (and many teenagers do experience depression), so unless you state otherwise, how do you expect anyone to know?

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Don't Regret Things You've Done Cuz
At The Time It Was The Right Thing To Do.

Have you've tried talking to her? It just sounds like she may be in denial that something is indeed wrong with you and she's afraid to confront it as well. It's hard to admit there's a problem, but as many people say, that's always the first step and it really does help to finally admit to it.

But the good part of this is that she had indeed noticed your change and just seems like she's not even sure how to handle it. As your guardian, she's not only being your sister but also your mother and father- not exactly an easy thing to do, as you probably already knew. Since I'm not sure how much older she is than you, I'm not sure exactly how to help you there to help you understand her side. But I'm hoping that this much does help anyway.

As a sister, she's doing the talking for you and putting aside your actual problem (my sis used to do the same and even accused me of faking an illness several times as we grew up). But it also seems as her motherly side does indeed see the problem and wants to help- she just isn't sure how to.

So just try to talk to her about it and see what you both can do to help make you feel better. Give her a helping hand to help her realize just how much you need her right now.