I'm not sure she should have treated the low T3 if your TSH was normal. T3 isn't as accurate of a test as TSH and it can actually fluctuate from blood test to blood test. The TSH is the actual measure of how much thyroid hormone your brain is telling your thyroid gland to make. Some doctors do treat people who are on the borderline for hypothyroidism if they have symptoms, but giving you more medication would probably make you hyperthyroid, causing more problems.
Perhaps seeing an endocrinologist would be a good idea to see if he or she thinks you have a thyroid problem at all or if you've been misdiagnosed.
What symptoms did you have before that are now better? What symptoms are you still experiencing? Also, how much Cytomel did the doctor give you?