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.
It's been a few months, but I remember a girl on the natural thyroid group I belong to who also had extreme hunger when she started armour. I think it was recommended to her that she start doing her Armour sublingually (either under the tongue or between inner cheek and gums)to keep it out of her stomach, and also start raising since 15 mg. was eventually going to cause her hypo to return (i.e. it was underdosing her). I don't remember if she switched to eating a low carb diet, but I personally like low carb diets when trying to lose weight! Armour is going to raise your metabolism and that's good! Good luck!