I'm thinking that the illnesses are due to a lowered immune system, and the low energy and forgetfulness could be from anemia and/or low blood sugar. These are common, and easily cured disorders.
Make sure your sister gets enough iron. Don't overdose on iron pills; she can develop problems that way. She needs red meat, liver, oysters, raisins, grape juice, and kelp. And the recommended dosage of Chelated Iron. Be sure and get chelated, as the other types aren't digested by the body properly. See if that helps her energy at all.
Secondarily, the only way you can tell if she has low blood sugar is to have a test done. Is it possible for her to see a doctor? If so, have her blood tested for hemoglobin count and a blood sugar test. I think they might even have tests for that over the counter, with the diabetic supplies. Ask your pharmacist.
And make sure she's getting a little sunshine (not through a window) each day. SAD can affect immunities. If it is impossible to get her outside, get a grow light bulb, in the gardening departments, which gives off the full spectrum of light, and put that in her room or lamp.
Now, as for stones: I think you need stones to boost immunity and strength. I'm not sure on those specifically, but I could guess citrine, gold, and quartz crystals (good for everything).
I hope your sister gets better soon.