You need to insist on further testing, particularly, Free T3 and
Free T4 to see where those levels are at. Those are the actual thyroid hormone levels, with Free T3 being the most important because it's the biologically active hormone, that correlates best with symptoms.
Your TSH, at 2.89, is still at the high end of the scale, and
while TSH should never be used as the sole tool for
diagnosing or treating thyroid disease, that's all we have right now.