Your doctor has no clue. First thing is that TSH is usually suppressed below range when taking a full daily replacement dosage of thyroid med. That does not mean hyperthyroidism, unless you have hyper symptoms due to excessive levels of Free T4 and Free T3, which you say you do not have. The TSH is suppressed because of taking the med in a short time, as compared to a slow, continuous flow of thyroid hormone in the natural state. Clearly your doctor doesn't understand this and is misinterpreting your suppressed TSH as hyperthyroidism. The second thing is that it is okay to alternate doses of T4 med because of the long half-life; however, it is quite a different matter with T3 med, which has a very short half -life. The med dose of any med with T3 should be consistent from day to day.
From what you have said I can't tell if your dosage was adequate to relieve symptoms, before the reduction. Clearly the reduction is adversely affecting you, with all thos hypo type symptoms.
A good thyroid doctor will treat a hypothyroid patient clinically by testing and adjusting Free T4 and Free T3 levels as needed to relieve symptoms, without being influenced by resultant TSH levels. Symptom relief should be all important, not just test results. If you ant you can click on my name and then scroll down to my Journal and read at least the one page Overview of a paper on Diagnosis and Treatment of Hypothyroidism: A Patient's Perspective. There is a link to the full paper. You may be able to use the Overview to persuade your doctor that the reduction was incorrect and at least return to your prior dosage.
You will also be interested in a recent scientific study that for the first time quantified the effect of Free T3 on hypothyroid symptoms. They concluded that, " Hypothyroid symptom relief was associated with both a T4 dose giving TSH-suppression below the lower reference limit and FT3 elevated further into the upper half of its reference." Following is a link.
By the way, hypothyroid patients are frequently deficient in Vitamin D, B12 an ferritin. So you should make sur e to get those tested and then supplement as needed to optimize. D should be at least 50 mg/mL, B12 in the upper end of its range, adn ferritin should be at leasst 100.
So I suggest that you use all this info and try to get your doctor to change his mind. If he refuses, then you will need to find a good thyroid doctor that will treat clinically, as described.
I'll just add a quick comment to what Gimel said. When we hear this: "labs show my TSH as hyperthyroid," we know right away that the doctor is not familiar with using Armour. Your TSH is very low because you are taking Armour (NDT). This is characteristic of NDT, it drives your TSH very low even with lowish doses of NDT because it contains T3. Your very low TSH does not mean you are hyperthyroid. It takes high FT4 and high FT3 to indicate that you are hyper. Doctors are not aware that NDT does this because they mostly prescribe Synthroid (which is T4 only). Synthroid does not make your TSH go low like Armour does. It's odd that after taking Armour for 10 years that your doctor is just noticing your low TSH (or maybe you've gone to a new doctor.).
Search for this: "19 Mistakes Patients Make (or their Doctors make for them!)" when using NDT. Look at mistake number 3, which is exactly what you are facing. Far be it from me to recommend it, but other people in this situation have gone out and got a big refill of their prescription and went back to their previous dose.