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Since your daughter is 14 years old and undergoing hormonal changes in body, the spider veins can be the result of these changes. Too much exposure to sun in fair skinned can be another cause. At times they are hereditary.
Spider veins can also be due to deep vein thrombosis of the deep veins of the leg or maybe valvular dysfunction of the deep veins of the legs. This can be diagnosed by color Doppler or by angiogram of the leg veins.
Diabetes, hypertension (she has this—white coat syndrome), abnormal kidney function can be precipitating factors.
However on net and without examining it is difficult to give a confirmed opinion. Please consult your doctor about these possibilities. Hope this helps. Take care!
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