Sleep: Find time release, keep looking, melatonin. I find that Rx trazodone works well for sleep. It is very inexpensive at Walmart USA, 150mg 360 tablets, one year supply, $40 cash price. Start at 50mg. You can get a smaller amount for a trial.
Body temps: Please also check mid-afternoon body temps that are going to respond to your morning doses of thyroid meds. Early morning body temps will not be so useful as a medication guide. You may need to push TSH very low below 1.0 to loose hypo symptoms.
Please get back on fish oil, it is needed by the brain.
Prolactin is not causing low LH/FSH, thyroid might.