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My girlfriend is not feeling well right now and she told me it's because of her mental state. And she need some time to work through things. I'm really trying to give her space but I'm terrified she's going to think I'm not here for her and break it off

If she’s asked for space then she wants space. She’s not going to be thinking “why has my girlfriend given me what I’ve asked for wow she doesn’t care at all.” I know it may be hard because you currently feel like you can’t be there for her right now, because she’s not letting you be, and so your projecting how you feel about the situation on to her, thinking that she must feel it too. She knows you’re there if she needs it, and right now that’s what she needs and it’s okay.