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With information which you have given she has high TSH with normal T4 level, she may be having hypothyroid state along with anemia
Her symptoms of loss of appetite may be reason for weight loss
cold hands supports hypothyroid state.Other features include rough skin and swelling delayed menarche
or irregular periods
Contipation may occur
Please visit to a Physician/Endocrinologist
for proper assesment and know if she has something else.
Once diagnosis is confirmed she can be treated with thyroid supplementation and such patients improve in few months time it is also important for the growth also at this age.
Hope this information helps you.