In evaluating thyroid related test results you should always compare to reference ranges shown on the lab report, so please give us those ranges. Also, what symptoms do you have? What have you been diagnosed with, that has resulted in taking all those meds?
Are you currently on a replacement thyroid hormone medication? If so, which one, what dosage and how long have you been like it?
Are the T4 and T3 tests for Free T4 and Free T3 or are they Total T4 and Total T3? They aren't same tests and don't provide the same information... Can you also please post the reference ranges for the T4 and T3 tests? Reference ranges vary from lab to lab so have to come from your own report. Your T4 seems to be high in the range, but your T3 may be low; of course, that depends on the ranges.
IGA test, typically is the one used to test for celiac disease. There are more thyroid antibody tests you should have - TSI to test for Graves Disease and TgAb to fully rule out Hashimoto's.
What, if any, symptoms are you experiencing? That's the biggest determination of whether yo9u're hyper or hypo, but then some symptoms can apply to either/both.