Just to clarify - IS that a FREE T4 and FREE T3, or is it total. Just saying T4 leads me to believe it might be total. If it doesn't say "free" or FT on the lab report, it would be total, which is considered obsolete and of little value.
I totally agree with everything gimel said and I'm one of those he referred to with suppressed TSH; mine stays at or below 0.01 all the time, but isn't an issue, so long as my FT's stay in line.
By the way, I meant to agree that your FT4 was high and needed adjustment, and for the future I hope I made it clear that you need to adjust based on symptoms and FT3 and FT4 levels, not TSH. Also, you didn't mention any FT3 results. Did you get tested for FT3 as well?
TSH is a pituitary hormone and it is affected by so many variables that it is inadequate as a diagnostic by which to determine medication and dosage. It is far better to test and adjust levels of the actual, biologically active thyroid hormones, free T3 and free T4 (not total T3 and total T4), as necessary to relieve symptoms, without being restricted by resultant TSH levels. Symptom relief should be all important, not TSH level. In fact many members taking thyroid meds report having a suppressed TSH level. that doesn't mean that you have become hyper, unless you have hyper symptoms, caused by excessive levels of FT3 and FT4.
For these reasons you need to continue to test and adjust FT3 and FT4 levels as necessary to relieve symptoms. If your doctor continues to emphasize TSH and is unwilling to treat you clinically (for symptoms), then you will have to find a good thyroid doctor that will do so.