I also have a feeling of something tight squeezing my throat sometimes as well, over my thyroid.
In the untreated state, your body was used to a continuous low flow of thyroid hormone from the gland. When you take the replacement thyroid dose all at once, it spikes the FT4 and FT3 for a short time, and thus suppresses TSH for most of the day. Most hypothyroid patients taking thyroid med like you find that when the dose is adequate the TSH is usually suppressed below range. A suppressed TSH does not mean hyperthyroidism unless there are hyper symptoms due to excessive levels of FT4 and FT3. My own TSH has been suppressed to about .01 - .05 for probably 40 years without ever having a hyper symptom.
A good thyroid doctor will adjust FT4 and FT3 levels as needed to relieve symptoms without being influenced by TSH levels. TSH has only a weak correlation with FT4 or FT3, and a negligible correlation with hypo symptoms. You go to the doctor because of having those hypo symptoms. The objective of treatment should be to alleviate hypo symptoms, not just adjust your TSH to a level the doctor likes. If you were now truly euthyroid you should not have hypo symptoms still.
Before commenting further, please tell me if you took your med before the blood draw for those tests, and if so, what time did you take the med, and what time was the blood draw?
Okay, so I'd say your FT4 is fine. Your hypo symptoms are due to your FT3 being too low. Typically for symptom relief FT4 needs to be around the middle of the range and FT3 in the upper half of its range, and adjusted from there as needed to relieve symptoms. In addition, hypothyroid patients are frequently too low in the range for Vitamin D, B12 and ferritin. So you need to get those tested and supplement as needed to optimize. D should be at least 50 ng/mL, B12 in the upper part of its range, and ferritin should be at least 100.
If you want some info to give your doctor, the following link is a study that quantified for the first time the effect of FT3 on symptoms. When you get to the link, scroll down and click on Fig. 1C. The data are in pmol/L, so the range is 3.1 - 6.8. The curves show the average effect of different levels of FT3 on symptoms.
If your doctor refuses to consider an increase in your T3 med, and gives you a lot of concern about a resultant suppressed TSH, I can give you data to refute that, if needed.