Something is affecting her nervous system, the most likely thing is a mineral/vitamin deficiency. Infections can also affect the nervous system.
Vitamin b, liquid drops under the tounge twice a day will help. Make sure she gets some b6, b12, in the complex, and some b5 in there as well. Vit b is depleted in those who eat a good amount of sugars and carbohydrates. It may be good to try to cut some carbs back and do more meats/ veggies.
Magnesium (also destroyed by high carb and sugar diets) also supports the nervous system, (low MG means increased adrenaline) and is usually very low in most american diets. Magnesium citrate is a quick absorbing form. A product called kidcalm is available online that gives dosing suggestions, or you can get MG citrate (or MG malate) at the health food store. These products can cause a loose stool, you just cut back the dose a little until they get used to it. I would also do an epsom salt bath 3 x a week. (2 c of salts to a warm bath, soak a half hour) before bed to calm the child and impart a bit of drowsy. (After she stands up in the bath rinse the epsom salt off or she might itch)
A third support for the nervous system is water- nerves run on hydro-electricity. The body is set up in such a way that if you go into any kind of dehydration, even slight, the water that normally supplies the nerves , skin and colon starts getting redirected to vital survival organs like the brain, which is 85% water and MUST retain that amount. Hence, dehydrated people get "nerves", may want to chew on fingernails, lips, pencils, get headaches, edgy and cranky, etc. Put a pinch of IODIZED sea salt in the water to help with absorption.
Another possibility is low iron, but DO NOT give iron supplements without a clear test of deficiency, because overdose of iron is EASY to achieve in young children and quickly lethal. Anyway, people who are anemic will chew on ice like crazy. They also have pica, which is the desire to chew/eat odd things. Sometimes bacterial infections in other parts of the body will cause anemia- because Bacteria syphons off the host's iron- it needs it to survive and replicate.
I beleive another thing that can cause tension in the nervous system is a yeast overgrowth in the gut. Cutting down the amount of milk taken can greatly help this. Yeast LOVES milk. Also there are other things the health food store can recommend for yeast . Xylitol is a sugar that we use- it is a 5 chain birch tree sugar, meaning yeast and bacteria eat it thinking they can, but then they can't digest it and die. This tastes surprisingly like sugar, It has NO aftertaste like fake sugars.
Heavy metal buildup and parasites can cause nervousness as well. But I would start with these above and see if you make any leeway. You may want to try putting "bite no more" on her fingertips to help stop the habit while you support those nerves and build up her mineral levels.
Fulvic acid is another product that can help remineralize. It typically has around 60+ elements in ionic form, which are easily accessable to the cells.
If you wonder if it really helps- try putting a dose on a plant! Watch the new succulent green growth pop out the top in a day or two.
Teeth issues/pain might be another reason for chewing, but probably not as common as the above issues.