What is a T4 and T3 test used for in a patient with no thyroid?

I was diagnosed with Thyroid cancer in 2007, the doctors took out my thyroid and then treated me with an I-131 radiation treatment, in december of 2007. After that my TSH was all over the map. In 2009 having random blood test my thyroglobulin level was increasing and my TSH was decreasing again my oncologist felt that another dose of the I-131 radiation treatment was the way to go. now two years later i have been having some of the same symptom as before: extreme fatigue, out of control body temperature, sore throat, ear aches, thought process is not there.... etc