I am currently taking Armour to treat Thyroid disorder and my appetite is stronger than it has ever been. I want to eat constantly, am always thinking about food (because I am always hungry). My TSH was 1.3 and total T3/T4 were way under the range (drs didn't test free for some reason). I have never been this obsessed with food and it is driving me nuts - I have been trying to have lots of self control, but it is hard - have gained 3 pounds so far.

No it shouldnt be because of T3..these hormones normally control appetite and keep the metabolism up. T3 and T4 effects your metabolism and may increase your appetite also.

Hypothyroidism causes a loss of appetite, while hyperthyroidism an increase in appetite.

Your blood test seem to be at odds with your symptoms, and you should have you free T3 and T4 tested.