Is TSH the only thing your doctor is testing? S/he should also be testing Free T4 and Free T3, which are the actual thyroid hormones, whereas TSH is a pituitary hormone and an indicator, at best.
What, if any, symptoms do you have? TSH of 4.43 could indicate that you need a higher dose of your medication, but that depends on symptoms and Free T4 and Free T3 levels. If you have those levels, please post them, with reference ranges, which vary from lab to lab, so have to come from your own report for best comparison.