What cage is she in? the recommended is 80 x 30 x 30cm (I think? it's been a long time since I've been on here
) If her cage is too small, it can take some time for the stress to show through. I would upgrade to a larger cage, The Alaska cage, or a bin cage would be great.
A Hamsters behaviour also changes when they get ill. Biting is one of the signs, So I'm glad you're going to see to a vet about this too.
Has there been a period where you haven't handled her so much, or has someone handled her without your supervision? I find these things can set them off too, and make them a bit more skittish and set back in the taming process.
I hope you figure out what is going on soon and that you resolve the issue. It's always upsetting when our loved fur babies bites us.