Hypothyroidism Struggles

I am looking to see what others have done or are doing to lose weight with hypothyroidism

I want to an endocrinologist and he took me off of Armour for 3 weeks (it was suppose to be 6 weeks but I started having severe side effects) and had my levels tested. In that amount of time my levels are on the very low end for Total T3 and Free T4 and high overall on my TSH; I was hypothyroid. During those 3 weeks, I gained 13 pounds despite exercising 90 minutes everyday and eating 1200 calories.

He switched me over to Levoxyl after looking at the labs and the weight slowed and is now maintained.

I asked about cytomel in addition to the Levoxyl(because I used Cytomel in the past for my RT3 and it helped with my symptoms), but he said he didn't like Armour or Cytomel because they were "feel good" medicines and old treatments.

-5'3 145 pounds (use to be 5'3 120-125 pounds)
-Managed hypothyroid (50mcg levoxyl a day, though with the recall I started synthroid)
-Eating 1200 calories a day
-Exercise 4-5 times weekly 45-90 minutes (aerobic and weights training)
-I eat gluten-free, low-carb high protein diet as my preference to foods
-Still have symptoms of hypothyroidism, despite level being in range (fatigue, depression, impaired memory, dry skin, muscle aches/fibromyalgia(dx), though I have severe insomnia)
-Female hormones(estrogen and progesterone) checked and was told those were normal

Is there something I am missing that could be causing the stubborn weight? I've been working at this for over 2 months. I am still not losing weight. I am desperate, depressed, and cry a lot about it because I am SO discouraged.