I went months without being able to eat, and if I did manage I would just throw everything up. It was awful and I lost a lot of weight.

What is your grandmother's physical state like? Is she otherwise capable, does she have some extra chunk on her, etc? People can go a very long time without eating if they're "prepared" for it. I was worried at my worst points I would need a feeding tube because I was going 4-5 days without even at attempt at food. But since my labs were fine and I had room to lose weight, they didn't do any interventions or make me eat which would cause significant discomfort. In fact, it ended up being helpful in a weird way because my body would get rid of fluid.

I really hope your grandmother gets the help she needs, I guess I share my story to help soothe you that if she can't get down food until next week it may be OK (depending on her specific circumstance).

I never found a food that was tolerable. I would highly recommend avoiding spicy foods or anything brightly colored, because coming back up is unpleasant. Have her eat very small but frequent meals, so they do not exceed the limited space she has in her stomach and she has time to digest. Unfortunately the vomiting isn't due to stomach acid like traditional GI issues, so eating only rice/white bread/etc isn't as helpful. It's more about the physical space available.