Thank you for your query at DoctorSpring.com
I understand your concern.
Thyroid hormone abnormalities are a little tricky to diagnose. In most cases, TSH is the most important parameter. A high TSH with normal T3, T4 or low T3, T4 levels indicate that the patient has hypothyroidism. TSH is stimulated by a feedback mechanism, hence if the thyroid values are intrinsically low, then TSH will shoot up leading to stimulating the thyroid hormone further increasing the output. In hyperthyroidism, TSH will be low, and T3, T4 will be high.
So your GP is right, in explaining that TSH is more important than the values of T3, T4 which actually varies throughout the day.
You can attach your reports for me to review and I can guide you accordingly.
Hope this was helpful,