If she needs time to think, then giving her time to think is definitely a good idea. Time to think might help you too (or it might not help you-- I don't know either way.)
If you have no-one else but her as a friend, that is hard for you, but it can also be hard for her. Being the only friend can feel like a big responsibility, and not all people are able to cope with that.
I do not know what the right answer is, but hopefully when she and you have time to think, you can both figure out what kind of friendship is right for the two of you, whether that be close friendship, casual friendship, or just nodding acquaintances-- I really do not know, but I do wish you luck (both of you) in figuring it out.