Sounds like you have a doctor like the one I dumped 2 back. TSH is within lab range so you should be just fine. Yeah, sure. He figured that as long as it dropped under 5 I should be fine and my symptoms must be from something else. The endo came next and said I was greatly undermedicated at 25 mcg of Synthroid and bumped me up to 88 mcg. He was content when my TSH hit 3.8 because my free T4 was 2.2 (range .6-2.2). I wasn't.
My current doc (bless her soul!) who wants to see free T3 values, put me on 2 grains of Armour to start. My latest labs show my TSH at .11 (.4-5.5), hyper by most standards, but my free T3 and free T4 are still very low, so she has given me the go-ahead to move up to 4 grains. The wonderful side effect from finally getting up to a more normal range for me is that my cholesterol and LDL levels have dropped 37 points in the last 3 months with no cholesterol drugs and no change in diet. Everyone should find a doc as sensible as mine.