Have an MRI done on your pituitary gland.
Yes, normally it would be expected that a high free T4 would go with a lower TSH; however, TSH is a pituitary hormone, that is affected by many variables and doesn't correlate very well to free T3 and free T4 levels. By the way, I would suggest that you ask that free T3 be added to your thyroid testing in the future. Free T3 is the most active thyroid hormone, that largely regulates metabolism and many other body functions. It is four times as potent as free T4, and it correlates best with hypo symptoms.
Speaking of symptoms, please describe any symptoms that you think might be related to thyroid.