I would work with the idea that her comment about finding something that feels okay has to do with your level of distress, not hers. I would also accept that she says there's no need to keep apologizing.

And then try to find something else to occupy yourself for the weekend and not email back that you are upset over the idea that she might be upset. It will probably not help because then you will be upset that that email was too much and be tempted to email an apology.