Yes, you do sound as if you'd benefit from a trial of thyroid hormone, now, not later. Your TSH is about where mine was when I started treatment.
The metallic breath business may be related. Does anyone else smell it, or is something only you perceive? Smell and taste aberrations are among the definite but lesser-known hypothyroid symptoms.
Don't give up hope! If my advice does nothing for you except to give you courage to persist in finding a diagnosis and treatment, my time giving it will have been well spent.