Thyroid hormone treatment (of any variety) can increase appetite -- it can also increase (restore to normal for that individual) metabolic rate -- the problem sometimes is that the increase in hunger excedes the increase in metabolic rate causing weight gain. A low carb diet is not a advisable with the high cholesterol - it may work in some cases, but a traditional low fat diet combined with avoiding simple sugars (ie, the obvious plus excessive rice, bread, pasta, potato) is recommended -- also it is more sustainable than some of the well-marketed fad diets --- above all, calories still count!
While some may suggest that the armour dose be increased until symptoms resolve independent of labs, I do not endorse this practice and would prefer to see the TSH level around 1.0 in my hashimoto patients.
Hope that helps -- sounds like the weight is a major problem and with the fatty liver & high triglycerides I would ask your doc about "insulin resistance" and consider aggressive screening (ie, glucose tolerance test) for diabetes or pre-diabetes.