Child's Dark Circles under Eyes and Diarrhea

My daughter who is almost 8 years old has had dark circles under her eyes since she was about 2 ?. They are usually red and sometimes purplish. They start in the corner of her eyes near her nose and extend down and then under her eyes. Also, her eyes are often a bit swollen especially when she first wakes up in the morning. Even when the swelling-look goes away, she still has the dark circles. This make her look very tired and people often comment that she looks tired. Even when she sleeps enough she still has them.
From everything I have read it sounds like allergies of some sort. What is the best way to go about diagnosing this? Should I assume it is food-related and start with eliminating certain foods? Could it be environmental? Should I add some sort of herbs or special vitamins?
She is almost 8 and is bit thin for her age ? she weighs not quite 50 lbs. She seems to have s sensitive digestive system in that she will have occasional bouts of diarrhea or loose bowel movements very easily. But I have never attributed it to anything in particular. I do not make her drink milk for 2 reasons ? she does not like it very much and I have read that dairy can be a common allergen. However I let her eat yogurt, because she really likes to eat that, and I let her eat any other foods that have dairy in them. I let her eat pretty much what she wants. She does not have a big appetite but she is willing to try lots of different foods.
She is bright, a good student, and seems to have lots of energy although at school she says she is sometimes very tired. When I have volunteered in her school I have sometimes noticed that she looks very tired and spacey and is a bit distracted easily, but she does not disrupt the class. But after school all she wants to do is play and play.
If you have any thoughts or a good idea of where to start I would very much appreciate it.

This does sound as though your daughter is suffering from allergies or food sensitivities. We have answered a question previously about dark circles under the eyes. Please see our website, www.richters.com. You can link to the item from the following address:
richters.com/questions-and-answers/02-19990302-3
In this item, I have listed the common food sensitivities that can cause this problem. Eliminating suspected foods from the diet is the best way to test for sensitivities. I recommend testing for sensitivities by substituting soy products for dairy products and rye bread for wheat bread. I now do not recommend soy products, because they are very difficult to digest, and many people are allergic to them. Substituting rye for wheat will not solve the problem if the person is sensitive to gluten. Rice and products made with rice are better substitutes for dairy products and wheat. Whole grain rice is very nutritious and easy to digest.
I recommend that you consult with a medical doctor about your daughter's diarrhea. Slippery elm bark powder is often effective for diarrhea, especially in gluten intolerance. Mash half a banana with one tablespoon of slippery elm bark powder, three times daily. Slippery elm soothes and the digestive tract and protects it against inflammation.
Because your daughter's digestion is not optimal, she should be eating only the most nutritious food, to give her the best chance of digesting the nutrients she needs for health. Eliminate all white, non-nutrient foods (foods with white sugar or white flour), any junk food, soda pops and even juices. Whole fruit, vegetables, grains and good quality meat and fish (not pre-coked or pre-processed) offer the best nutrients.
When you eliminate dairy from your daughter's diet, you must eliminate ALL dairy. Even a trace of dairy in a food will set up the allergic reaction if she is sensitive to dairy. Yogurt is often well tolerated, even when a person is allergic to dairy. This is because the dairy is "pre-digested" by the bacterial cultures in yogurt. I suggest that you continue with yogurt because your daughter's digestive weakness appears to need the help of bacterial cultures. Make sure that the yogurt is a good brand with active bacterial cultures and without sugar. If your daughter needs the yogurt sweetened, add your own fruit, and if necessary, a little honey.