I have the symptoms but Doctors are doing nothing

Thyroid problems run in my family so after four years of suffering from very dry peeling skin, hair which falls out in handfulls, tingling hands and fingers, weight gain and inability (despite dieting) to lose it, extreme fatigue and depression I asked my doctor for a thyroid test

I was given remote access to my medical records to view the results and they were listed with other historical tests as follows: T4: 12.9, 13.3,11.4, 10.6 and 10.7

My TSH seems normal though the last test recorded it at 4.28.

My doctor says my results are still within normal limits so although I am sitting at the low end of normal and my symptoms are severe, they are not being treated. Please can someone offer any advice. I am pretty desperate. Are there any further investigations I can have? Has anyone else the same problems?

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