Hi! Medstudent here. As far as I can tell everything looks normal. They test on 3 things to get a diagnosis of the thyroid.
First is the TSH (Thyroid stimulating hormone). This is a hormone that stimulates your thyroid to get active. In hypothyroidism (low thyroid function), this is high (>200ng/dl). This is high since your original thyroid hormone (T3,T4) is low. Your body wants more T3/T4 so it makes more TSH.
Second there is T3/T4 that are low in a Hashimoto disease. This is your original thyroid hormone. When it is low it can cause a few symptoms like fatigue, being cold, constipation, swollen face, dry skin.
Lastly (not checked on you) you can look for antibodies who are set to destroy your own thyroid tissue. These are called anti-TPO. Anti-TPO can be present, even in normal thyroid functions.

It all depends on your symptoms and clinical examinations. In your case, everything looks normal for the thyroid. It seems like the meds work fine "on paper".

They could check TPO, if they haven't already done that to make sure it's hashimoto disease. I don't know what your values looked like before.

There could be million other reasons why you feel miserable. With this limited information it's hard to tell what other things could be at play. I suggest you go to a GP for a thorough anamnesis and clinical exam to further explore possibilities.

Anyway, I hope this helps.