Do you know the actual test result numbers, so that you can evaluate them against the ranges yourself, and not just be told "they are fine"? If not, I suggest this as a first step to taking control of your own health. I also suggest that you take your basal body temperature. Many years ago BBT was shown by Dr Broda Barnes to be a very reliable indicator of metabolism and thyroid levels. Take the BBT in your armpit, before getting out of bed. Dr. Barnes established a normal range of 97.8 -98.2. The lower you are below 97.8, the greater the need for medication. If you want to read about this there are many references on the net. Look for Dr. Broda Barnes. Please post results so other posters can pick up on this.
If the levels are stable (goal is TSH 0.5-2.5) then would be hard to pin the symptoms on the thyroid. Staying on the same dose is not uncommon...
If the generic is keeping levels consistent, then there is no definite benefit from switching back to a brand in most cases, but that would not be unreasonable.