Our DD used to have purple/redish circles under her eyes.
We cut out all dairy and they did go away.
After 1.5 yrs off dairy we have added a bit of cheese and a bit of yogurt back into her diet and she is doing fine with it.
We give her almond milk when she has milk, like for cereal.
Cutting out dairy was hard at first, because she ate it all. the. time.
But after a couple of weeks it got much easier and se got used to eating other things. Found out she LOVED cubed avocado. It is soft and creamy.