Hi, Jaime:
Synthroid is thyroid hormone. I know that sounds like a dumb statement, but what I mean by it is that the Synthroid acts exactly like thyroid hormone, and if you get too much of it, you can be hyperthyroid (which may have happened when you were dropped from 150mg to 112mg). Also, if you take too little of it, you could be hypothyroid. You should not expect to actually be hypothyroid if you are on the correct dose.
Night sweats may have any number of causes besides excess levels of thyroid hormone. I don’t know. If it were me, I would make an appointment with my doctor to get my TSH levels checked again, and if all was still well in that area of things, I would ask the doctor what else might be going on.
Wishing you well.