Hi Gina. Welcome to MN!
What a lovely post. I do hope that you will get some helpful suggestions here.
I have suffered from depression (am having a bad day today too!) The most valuable thing that you can do, I believe, is to hear how your relative is feeling. Try to reflect back to her what she might be saying when she says that she doesn't feel well/doesn't feel like eating:
You: How are you today? Would you like something to eat.
Her: No thanks. I feel awful. These stomach pains are grim.
You: You are feeling low today. It must be frustrating still to feel ill.
Even if the pain is "all in her head" it will be very real for her. Saying that she has stomach pains may be the only way which she can find to describe a whole range of confusing emotions, which she may well not understand herself. One of the frustrating things about depression for me is that it takes away your ability to really understand how you are feeling yourself. It's such a relief when someone else can put it into words.
If you haven't already read it, can I recommend "How to talk so that kids will listen, and how to listen so that kids will talk." Although it's not specifically about depression, the techniques in it are brilliant for talking with someone who is depressed. It's also useful reading for any parent!
In the meantime, try to find something that she fancies to eat. Scrambled eggs/boiled eggs are good comfort food and very easily digested. Suggest making some for her specially - she will feel cared for/loved, even if she says no. Build up drinks are also a good idea.
Suggesting a regular walk is also good, if she is awake long enough. It will get you both out of the house (it can be hard for you, living with/being trapped indoors with someone with depression) and a short walk in real light - even gloomy drizzly weather like today - every day, will do someone wonders. Perhaps you could suggest a walk to the library to choose some books if she is up at night. She may value something to read in the long hours.
HTH