I had quite a few of those symptoms from hypothyroidism. When my TSH hit the mid 3's I gained weight though.
Your TGab is elevated, which is often a sign of Hashimoto's thyroiditis. While Hashi's is ultimately hypo, in the early stages it can be hyper or swing from hypo to hyper. Also, TGab can be somewhat elevated with Graves' disease (hyper). TSI (thyroid stimulating immunoglobulin) is the definitive test for Graves'.
Right now, your TSH is a little high. AACE recommended many years ago that the TSH range be adjusted to 0.3-3.0. As you can see, your lab and most others have been very slow to adopt that change. So, your TSH indicates hypo. Your TSH being so high virtually eliminates Graves' as a possibility. Your FT4 is at 63% of range, which is just a bit high of the 50% guideline for FT4. So, it looks like your thyroid is still producing enough FT4.
Did they test FT3?
Have you had a thyroid ultrasound?