Hi,
I've got a couple suggestions. If the antibiotics are not working, it may not be a bacterial infection. In which case, the antibiotics won't help, and trying different kinds back to back, will only weaken her own defense mechanisms. So boosting her natural defenses should be the first thing to do. Giving her plenty of fluids, watered down juice with a pinch of sea salt will help to hydrate her. Echinacea extract in the glycerin children's formula at any health food/co-op. Garlic, raw! give a spoonfull of minced with honey- I know she may not like it, dont force it on her.
Next, the dark circles may not be from lack of sleep, but from allergies to foods, especially DAIRY. cut out ALL forms of dairy. No other heavy foods, like breads. Gluten is hard to digest even if we are not allergic- but if we are, dark circles under eyes is a give away- they call it allergy eyes. Food allergies that are not corrected will make glands over work, and can make them swell up. Soy is another big one. Soy is in a lot of processed foods, just feed whole foods, fresh fruits and veggies. Rice and peas is my daughters comfort food, and its easy to digest. No red meats now until she is better, either. Just think: easy for the digestive system to process, so the immune system can work harder.
Also, there is an herb you can make an infusion with (tea) its called CLEAVERS. it is especially helpful in moving lymph through the system, and clearing up clogged swollen glands. Go to any place you can get bulk herbs, and ask for it. You may want to make an herbal mix with cleavers- something soothing, chamomile, passion flower, lemon balm....
Good luck! Stop taking her to the Dr. for now, its obvious they are not solving the problem, and besides she, and you, are only chancing on the exposure to more illnesses every time you step into the clinic.
Check out this book:
http://www.amazon.com/Naturally-Healthy-Babies-Children-C...
Its called Naturally Healthy Babies and Children, by Aviva Jill Romm. It has been my savior, and we hardly ever need to go to the Dr.'s office.
Good Luck
C.