Not sure where you live, but you do sound like a classic subclinical hypothyroid, and it might benefit you to change doctors. The phrase "my doctor is completely uncooperative" is a big alarm bell! There are doctors who do specialize in thyroid conditions, know that the current baselines for "normal" are screwed up and outdated, and will be open to trying things to fix your symptoms - plus get at the root cause of why your thyroid is underperforming and what's realistic to do about it.
I don't have your metabolism concern, but everything else I can match you step for step. My TSH is perfectly normal too. But oddly enough (

) the lowest dose of Armour has resolved my dry skin, poor sleep, fatigue, constantly feeling like I'm going to freeze to death, and brain fog. It takes the right doctor. With some creative accounting, they code one of my two followups per year as a physical, so that's covered. The Armour is discounted via my current insurance (it's really inexpensive anyway), and some of the bloodwork is covered. I found my doctor via Mary Shomon's recommendations and links.
Good luck - and don't give up. Life with a fully-supported thyroid is pretty amazing and is worth pursuing.