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Being in Canada, it is most likely that your T4 of 13.2 is Free T4, with a typical range of about10.2 - 19.2 pmol/L. Similarly I expect that your T3 of 3.7 is Free T3, with a typical range of about 3.5 - 7.7 pmol/L. Assuming that is correct, then your FT4 would be only 33% of its range, and your FT3 would be only at 4.8% of its range. So your results are certainly not high enough to cause the low TSH. Plus the doctor reacted and reduced your med in the erroneous belief that you had become hyper; however, I am sure you are not experiencing hyper symptoms, but instead hypo symptoms. It was the dosing, not the dose that suppressed TSH and resulted in the doctor reducing your med dosage.
Add to that the fact that those ranges are too broad, and skewed to the low end because only patients with high TSH are excluded from the database from which ranges are calculated by the labs. This means that undiagnosed hypothyroid patients and also hypothyroid patients on thyroid med can all be included in the database.
Also add to that the fact that everyone can have different levels of FT4 and fT3 at which they feel normal. Since there is no biochemical test that reliably defines a patient's thyroid status, the only effective way to diagnose and treat a potential hypothyroid patient is a full medical history, an evaluation for signs/symptoms typical of hypothyroidism, and expanded testing for FT4, FT3, TSH is useful only to identify overt primary hypothyroidism (diseased or damaged thyroid gland), Sometimes Reverse T3 (RT3), cortisol, and Vitamin D, B12 and ferritin.
So your doctor has to understand about TSH suppression from once a day dosing. Point out that your FT4 and FT3 are below mid-range, so you are clearly not thyrotoxic. (By the way, you should make sure to always defer your morning thyroid dose until after the blood draw to avoid false high results. You can find references for all this in the link in the Overview I mention below. The doctor needs to medicate you by raising your FT4 to about mid-range, and your FT3 in the upper half of its range, as needed to relieve hypo symptoms. You also need to test and supplement as needed. Vitamin D is very important and needs to be at leasts 50 ng/ml, B12 in the upper part of its range, and ferritin should be at least 100.
If you want to confirm what I have said, 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.
Doctors don't seem to understand or accept that our bodies are used to a continuous low flow of thyroid hormone from the gland, and that taking a significant dose of thyroid med all at once spikes FT4 levels and to a lesser degree FT3 as well, resulting in suppression of TSH for most of the day. A suppressed TSH in that situation does not mean you have become hyperthyroid and need to have your med dose reduced, unless you have hyper symptoms due to excessive levels of FT4 and fT3.
Before further discussion, please post the reference ranges shown on the lab report for your thyroid tests.