I would get a new doctor for your son. Relating to his back pain, ask for a referral to a kidney specialist or a gastroenterologist.
Here is some information on fingertip eczema:
About Fingertip Eczema and Prevention
Fingertip eczema is a condition in which the whole finger or parts of the finger are affected by eczema's red, watery and bumpy patches. Fingertip eczema causes numbness, stiffness and burning in the fingers. Cracked and dry fingertips often result.
After fingertip eczema appears, the skin begins to peel off as it heals and continues peeling until all damaged skin falls off of the finger. This can continue with the same finger or may move from one finger or hand to another. While there is no cure for the condition, it can be managed.
To help control eczema, take great care to make sure the skin is sufficiently moisturized. Use non-irritating lotions and creams. Thicker creams are often the preferred option for eczema patients, as moisturizing with thick cream will allow the patient more time between applications. Aloe vera gel, calendula cream and lotions containing chaparral (a desert plant used topically in Mexican folk medicine for skin conditions) are all recommended. Use mild soaps to clean the hands, and shower or bathe as quickly as possible.
Maintain constant temperatures in the home. Use non-irritating laundry detergents, and avoid harsh cleaning preparations.
Keep smoking and consumption of coffee to a minimum, as both can irritate eczema. Additionally, cow's milk and cow's milk products should be eliminated from the diet, as should all hydrogenated oils and fats as well as trans fatty acids.
Treatment for Fingertip Eczema
Most physicians will prescribe anti-inflammatory topical medications, such as steroids worn on the hands at night under gloves, to keep the medication absorbed into the skin. Antibiotics or combined steroid and antibacterial medications may also be used.
Those with eczema may choose alternative therapies instead of medications for fingertip eczema. A paste of grated nutmeg and water can be applied daily to affected areas to help soothe and treat the skin. (Grate nutmeg and add a few drops of water until the shavings are moistened into a paste.) Other recommended home remedies include rubbing the juice of green leaves of finger millet on the area daily, adding 1 to 3 gm indigo naturalis to mild lotion to make a topical ointment for daily use or adding one tsp. of camphor oil to one tsp. of sandalwood paste to rub on eczema as needed.
Could also be similar to the cold sore virus and maybe contagious .does he suck his fingers .Are they blistered ?