I have hypothyroidism and hashimoto's. My current TSH is 0.01, T3 (liothyronine) is 169, and free T4 is 2.0. Doctor is concerned. What could be wrong?

Strange. If you have hypothyroidism and not taking a thyroid supplement, it's not clear how come your TSH is that low. It should be high > 4.5 at least by some new norms > 2.2. Your TSH suggests hyperthyroidism unless you are taking a thyroid supplement and taking too much of it. I think you need to discuss it with your doc in more detail.
Too much thyroid. Most likely - the thyroid med you are taking is at too high a dose. Least likely- your pituitary gland which also regulates your thyroid function has totally failed. Too much thyroid can cause a lot of problem such as weight loss, heat intolerance, tremors, bone loss, anxiety , palpitation etc.