You need an ultrasound of your thyroid if you haven't had one. Elevated TG is just one of many signs of possessing malignant cysts/tumor of the thyroid. I am not saying you have one, everyone has a different normal. BUT to be sure get the thyroid ultrasound run. Low cost, non-invasive, and quick. Antibodies tests are not 100%. The Hashimoto's TPOAb is as close as it gets with a 85-90% positive identification of hashimoto's.
FT4 1.22 (0.8-1.8) - [1.22-0.8]/[1.8-.8]*100 = 42% This is below optimal. Optimal is 50-80% with a narrower region for women of childbearing years needing to be in the 60-80% range of normal.
TSH levels can flux as a result of unstable hormone production and flux, the time of day you take the blood draw.. diet etc. But normal range is 0.3-3.0 for TSH now. And most GOOD thyroid MDs consider a TSH above 2.5 to be suspicious and borderline thyroid failure. Optimal TSH is between 0.89-1.1 which implies around 1. Treatment is a good call. I would just want the US if I was you.
To rule out adrenal issues you need some blood work and other tests run. ACTH and cortisol 8 am fasting blood serum tests, a DHEA sulfate blood serum, and a cortisol rhythm test (24 hour saliva or urine).
Also you should look into your B12, vit D, Mg, and ferritin levels. If you haven't had the full chem spec panel in a while.. just get the works.
If you get all this done well we will be able to see if something is up.