Hello - Most patients do see resolution of symptoms once levels are in the normal range, but this can take some time, especially if you were hypER for a while.
Some patients *do* have symptoms with suppressed TSH, even if T3/T4 are normal.
Insomnia is SO frustrating, so definitely mention this to your doctor. The more specific you can be, the better. Are you having trouble falling asleep because your mind is racing? Or are you waking up repeatedly? Or all of the above?
Also consider “sleep hygiene” - here are some tips from Cleveland Clinic:https://my.clevelandclinic.org/health/diseases/12119-insomnia/prevention