How much space should i give her?

Well first of all your a good bf for not givin up on her yet, but if she' s not answering you normaly that means that she wants space. But right now she kinda needs to know that she has someone somewhere that she can lean on. If she found a lump in her brreast that is serious and she don;t know what to think right now. just give her some more time and if she still don't come around, leave her a text or some thing tellin her that your still goin to be ther for her when she needs her. She's just really stressed, i mean she has cancer so obviously she wuold try to find an outlet such as drinkin. But try to be patient with her, either she'll come around ,or she won't. leave the choice to her once you've said your part.